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#include <bits/stdc++.h> using namespace std; int n, answer; bool p1[2005], p2[2005], used[2005]; int x1[2005], x2[2005]; vector<vector<int>> g(1005); void dfs(int v) { if (p1[v]) { answer = v; return; } used[v] = 1; for (int i = 0; i < g[v].size(); i++) if (!used[g[v][i]]) dfs(g[v][i]); return; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int t; cin >> t; while (t--) { cin >> n; for (int i = 0; i <= n; i++) { g[i].clear(); p1[i] = 0; p2[i] = 0; used[i] = 0; } for (int i = 0; i < n - 1; i++) { int x, y; cin >> x >> y; g[x].push_back(y); g[y].push_back(x); } int k1, k2; cin >> k1; for (int i = 0; i < k1; i++) { cin >> x1[i]; p1[x1[i]] = 1; } cin >> k2; for (int i = 0; i < k2; i++) { cin >> x2[i]; p2[x2[i]] = 1; } cout << "B " << x2[0] << endl; int f; cin >> f; dfs(f); int ans = answer; cout << "A " << ans << endl; int f1; cin >> f1; if (p2[f1]) cout << "C " << ans << endl; else cout << "C -1" << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; const long long N = (5e5) + 322; const int INF = (int)(1e9); const long long mod = 998244353; const double eps = 1e-9; int n, m, test, used[1111], col1[1111], par[1111], col[1111], ver; vector<int> v[1111]; void dfs(int x, int p = -1) { if (col[x]) { ver = x; return; } for (auto it : v[x]) { if (it == p) continue; dfs(it, x); } } int getB(int x) { cout << "B "; fflush(stdout); cout << x << "\n"; fflush(stdout); int ans; cin >> ans; return ans; } int getA(int x) { cout << "A "; fflush(stdout); cout << x << "\n"; fflush(stdout); int ans; cin >> ans; return ans; } int main() { cin >> test; while (test--) { cin >> n; memset(used, 0, sizeof used); memset(col1, 0, sizeof col1); memset(par, 0, sizeof par); memset(col, 0, sizeof col); for (int i = 1; i <= n; ++i) v[i].clear(); for (int i = 1; i <= n - 1; ++i) { int x, y; cin >> x >> y; v[x].push_back(y); v[y].push_back(x); } dfs(1); int k1; cin >> k1; for (int i = 1; i <= k1; ++i) { int x; cin >> x; col[x] = 1; } int k2; cin >> k2; int start = 0; for (int i = 1; i <= k2; ++i) { int x; cin >> x; col1[x] = 1; start = x; } int cur = getB(start); dfs(cur); if (col1[getA(ver)]) { cout << "C "; fflush(stdout); cout << ver << "\n"; fflush(stdout); } else { cout << "C "; fflush(stdout); cout << -1 << "\n"; fflush(stdout); } } return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> g[1002]; bool vis[1002]; bool my[1002], chen[1002]; int dfs(int n) { if (my[n] == 1) return n; vis[n] = 1; for (int i = 0; i < g[n].size(); i++) { int v = g[n][i]; if (!vis[v]) { int ans = dfs(v); if (ans != -1) return ans; } } return -1; } void make() { memset((vis), 0, sizeof(vis)); memset((my), 0, sizeof(my)); memset((chen), 0, sizeof(chen)); for (int i = 0; i < 1002; i++) g[i].clear(); } int main() { int t, i, j; cin >> t; while (t--) { make(); int n, k1, k2; cin >> n; for (i = 0; i < n - 1; i++) { int u, v; cin >> u >> v; g[u].push_back(v); g[v].push_back(u); } cin >> k1; for (i = 0; i < k1; i++) { int u; cin >> u; my[u] = 1; } cin >> k2; for (i = 0; i < k2; i++) { int u; cin >> u; chen[u] = 1; } int q; for (i = 1; i <= n; i++) if (chen[i] == 1) break; cout << "B " << i << endl; cout.flush(); cin >> q; if (my[q] == 1) { cout << "C " << q << endl; cout.flush(); continue; } int ans = dfs(q); cout << "A " << ans << endl; cout.flush(); cin >> q; if (chen[q] == 1) { cout << "C " << ans << endl; cout.flush(); } else { cout << "C " << -1 << endl; cout.flush(); } } }
#include <bits/stdc++.h> using namespace std; const int N = 2000010, mod = 1e9 + 7; inline int read() { int x = 0, f = 1; char ch = getchar(); while (ch < '0' || ch > '9') { if (ch == '-') f = -1; ch = getchar(); } while (ch >= '0' && ch <= '9') { x = (x << 1) + (x << 3) + (ch ^ 48); ch = getchar(); } return x * f; } vector<int> g[N]; int vis1[N], vis2[N], get, d[N], p[N]; void dfs(int u, int pre, int dep) { d[u] = dep; for (auto e : g[u]) { if (e == pre) continue; dfs(e, u, dep + 1); } } void solve() { int n = read(); for (int i = 1; i <= n; ++i) g[i].clear(), vis1[i] = vis2[i] = 0; for (int i = 1; i < n; ++i) { int x = read(), y = read(); g[x].push_back(y); g[y].push_back(x); } int k1 = read(); for (int i = 1; i <= k1; ++i) { p[i] = read(); vis1[p[i]] = 1; } int k2 = read(); int p2; for (int i = 1; i <= k2; ++i) { int x = read(); vis2[x] = 1; p2 = x; } cout << 'B' << ' ' << p2 << endl; int p1 = read(); dfs(p1, 0, 0); int dep = 1e8, ans; for (int i = 1; i <= k1; ++i) { if (d[p[i]] < dep) dep = d[p[i]], ans = p[i]; } cout << 'A' << ' ' << ans << endl; int get = read(); if (vis2[get]) cout << 'C' << ' ' << ans << endl; else cout << 'C' << ' ' << -1 << endl; } int main() { int T = read(); while (T--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; long long int mod = (1ll << 63); vector<vector<int> > adj(1005); vector<int> dis(1005); int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); int t; cin >> t; while (t--) { int n; cin >> n; for (int i = 0; i < n; i++) adj[i].clear(); for (int i = 0; i < n - 1; i++) { int x, y; cin >> x >> y; x--, y--; adj[x].push_back(y); adj[y].push_back(x); } int k1; cin >> k1; vector<int> v1(k1); for (int i = 0; i < k1; i++) cin >> v1[i]; int k2; cin >> k2; vector<int> v2(k2); for (int i = 0; i < k2; i++) cin >> v2[i]; cout << "B " << v2[0] << endl; int st; cin >> st; st--; for (int i = 0; i < n; i++) dis[i] = n + 2; queue<int> qu; qu.push(st); dis[st] = 0; while (qu.size()) { int cr = qu.front(); for (int x : adj[cr]) { if (dis[x] > dis[cr] + 1) { dis[x] = dis[cr] + 1; qu.push(x); } } qu.pop(); } int mind = n + 1, vrt = -1; for (int i = 0; i < k1; i++) { if (dis[v1[i] - 1] < mind) { mind = dis[v1[i] - 1]; vrt = v1[i]; } } cout << "A " << vrt << endl; cin >> st; int yes = 0; for (int i = 0; i < k2; i++) { if (v2[i] == st) yes = 1; } if (yes) { cout << "C " << vrt << endl; } else { cout << "C -1" << endl; } } return 0; }
#include <bits/stdc++.h> const long long inf = std::numeric_limits<long long>::max(); const long long mod = 1e9 + 7; using namespace std; mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); stack<int> s; vector<int> g[1100]; int xx, yy; bool done; void dfs(int v, int p) { if (done) return; for (auto i : g[v]) { if (i == p) continue; if (i == yy || done) { done = true; break; } s.push(i); dfs(i, v); if (!done) s.pop(); } } int main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); int t; cin >> t; while (t--) { for (int i = 0; i < 1100; i++) g[i].clear(); while (!s.empty()) s.pop(); set<int> x, y; xx = yy = 0; done = false; int n; cin >> n; for (int i = 0; i < n - 1; i++) { int x1, y1; cin >> x1 >> y1; x1--, y1--; g[x1].push_back(y1); g[y1].push_back(x1); } int k1, k2; cin >> k1; for (int i = 0; i < k1; i++) { int v; cin >> v; v--; x.insert(v); } cin >> k2; for (int i = 0; i < k2; i++) { int v; cin >> v; v--; y.insert(v); } yy = *y.begin(); cout << "B " << yy + 1 << endl; cin >> yy; yy--; xx = *x.begin(); s.push(xx); if (x.find(yy) != x.end()) { cout << "C " << yy + 1 << endl; continue; } dfs(xx, -1); while (!s.empty() && x.find(s.top()) == x.end()) s.pop(); cout << "A " << s.top() + 1 << endl; int ccc; cin >> ccc; ccc--; if (y.find(ccc) == y.end()) { cout << "C -1" << endl; } else { cout << "C " << s.top() + 1 << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 11; vector<int> v[N]; int a[N], b[N], d[N]; int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int t; cin >> t; while (t--) { int n; cin >> n; for (int i = 1; i <= n; i++) { v[i].clear(); d[i] = -1; } for (int i = 1; i < n; i++) { int l, r; cin >> l >> r; v[l].push_back(r); v[r].push_back(l); } int k1, k2; cin >> k1; for (int i = 1; i <= k1; i++) cin >> a[i]; cin >> k2; for (int i = 1; i <= k2; i++) cin >> b[i]; cout << "B " << b[1] << endl; int x; cin >> x; vector<int> vv; vv.push_back(x); d[x] = 0; for (int j = 0; j < vv.size(); j++) { int l = vv[j]; for (int j = 0; j < v[l].size(); j++) if (d[v[l][j]] == -1) { d[v[l][j]] = d[l] + 1; vv.push_back(v[l][j]); } } int p = a[1]; for (int i = 1; i <= k1; i++) if (d[a[i]] < d[p]) p = a[i]; cout << "A " << p << endl; cin >> x; int y = 0; for (int i = 1; i <= k2; i++) if (b[i] == x) { y = 1; break; } if (y == 1) cout << "C " << p << endl; else cout << "C " << -1 << endl; } }
#include <bits/stdc++.h> using namespace std; const int maxn = 1000; vector<int> g[maxn]; bool was[maxn]; int n; set<int> s1, s2; void Read() { s1.clear(); s2.clear(); for (int i = 0; i < maxn; ++i) g[i].clear(), was[i] = false; scanf("%d", &n); int a, b; for (int i = 1; i < n; ++i) { scanf("%d%d", &a, &b); --a, --b; g[a].push_back(b); g[b].push_back(a); } int k1, k2; scanf("%d", &k1); for (int i = 0; i < k1; ++i) { scanf("%d", &a); --a; s1.insert(a); } scanf("%d", &k2); for (int i = 0; i < k2; ++i) { scanf("%d", &a); --a; s2.insert(a); } } int dfs(int v) { if (s1.count(v)) return v; was[v] = true; int ans = -1; for (int j : g[v]) if (!was[j]) ans = max(ans, dfs(j)); return ans; } void calc() { int start = *s2.begin(); cout << "B " << start + 1 << endl; cin >> start; start--; int v = dfs(start); cout << "A " << v + 1 << endl; int have; cin >> have; have--; if (s2.count(have)) cout << "C " << v + 1 << endl; else cout << "C " << -1 << endl; } void alg() { Read(); calc(); } int main() { int t; scanf("%d", &t); for (int i = 0; i < t; ++i) alg(); return 0; }
#include <bits/stdc++.h> using namespace std; vector<vector<int>> g; bool istree[1001], istree2[1001]; vector<int> tr1, tr2; int dfs(int u, int p) { if (istree[u]) { cout << "A " << u + 1 << endl; int q; cin >> q; if (istree2[q - 1]) return u + 1; return 0; } for (int i = 0; i < g[u].size(); ++i) { if (g[u][i] == p) continue; int x = dfs(g[u][i], u); if (x) return x; } return 0; } int main() { ios::sync_with_stdio(0); cin.tie(0); int T; cin >> T; while (T--) { int n; cin >> n; g.clear(); g.resize(n + 1); tr1.clear(); tr2.clear(); memset(istree, 0, sizeof(istree)); memset(istree2, 0, sizeof(istree2)); for (int i = 0; i < n - 1; ++i) { int a, b; cin >> a >> b; g[--a].push_back(--b); g[b].push_back(a); } int k; cin >> k; for (int i = 0; i < k; ++i) { int x; cin >> x; istree[--x] = 1; tr1.push_back(x); } cin >> k; for (int i = 0; i < k; ++i) { int x; cin >> x; istree2[--x] = 1; tr2.push_back(x); } cout << "B " << tr2[0] + 1 << endl; int q; cin >> q; int x = dfs(q - 1, -1); cout << "C " << (x ? x : -1) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; int H[1000], M[1000], P[1000], Lim[1000]; vector<vector<int> > edges(1000); queue<int> Q; void fill(int n) { for (int i = 0; i < n; i++) { H[i] = 0; M[i] = 0; P[i] = 0; Lim[i] = 0; } } void bfs() { while (!Q.empty()) { int a = Q.front(); Q.pop(); int n = edges[a].size(); for (int i = 0; i < n; i++) if (M[edges[a][i]] == 0) { M[edges[a][i]] = 1; H[edges[a][i]] = H[a] + 1; P[edges[a][i]] = P[a]; Q.push(edges[a][i]); } } } int main() { int t; cin >> t; while (t--) { int n; cin >> n; fill(n); for (int i = 1; i < n; i++) { int x, y; cin >> x >> y; edges[x - 1].push_back(y - 1); edges[y - 1].push_back(x - 1); } int k1, k2; cin >> k1; for (int i = 0; i < k1; i++) { int x; cin >> x; M[x - 1] = 1; P[x - 1] = x - 1; Q.push(x - 1); } bfs(); cin >> k2; int minil = 1001; for (int i = 0; i < k2; i++) { int x; cin >> x; Lim[x - 1] = 1; minil = min(minil, x - 1); } cout << "B " << minil + 1 << "\n"; int response; cin >> response; if (response == -1) exit(0); response--; if (H[response] >= k2) { cout << "C -1\n"; } else if (H[response] == 0) { cout << "C " << response + 1 << "\n"; } else { cout << "A " << P[response] + 1 << "\n"; int response1; cin >> response1; if (response1 == -1) exit(0); response1--; if (Lim[response1] == 1) cout << "C " << P[response] + 1 << "\n"; else cout << "C -1\n"; } cout.flush(); for (int i = 0; i < n; i++) edges[i].clear(); } return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 1000000007; const long long INF = 1e18; const int MX = 100001; int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int T; cin >> T; while (T--) { int N; cin >> N; vector<int> edges[N + 1]; int a, b; for (int i = 0; i < N - 1; ++i) { cin >> a >> b; edges[a].push_back(b); edges[b].push_back(a); } int k; cin >> k; vector<bool> mano(N + 1, false); for (int i = 0; i < k; ++i) { cin >> a; mano[a] = true; } cin >> k; vector<bool> jo(N + 1, false); for (int i = 0; i < k; ++i) { cin >> a; jo[a] = true; } cout << "B " << a << endl; int ans; cin >> ans; if (mano[ans]) { cout << "C " << ans << endl; continue; } queue<int> q; q.push(ans); int c; vector<bool> buvau(N + 1, false); while (!q.empty()) { c = q.front(); q.pop(); buvau[c] = true; if (mano[c]) break; for (auto u : edges[c]) if (!buvau[u]) q.push(u); } cout << "A " << c << endl; cin >> ans; if (jo[ans]) { cout << "C " << c << endl; } else cout << "C -1" << endl; } }
#include <bits/stdc++.h> using namespace std; char _; long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); } long long fpow(long long b, long long exp, long long mod) { if (exp == 0) return 1; long long t = fpow(b, exp / 2, mod); if (exp & 1) return t * t % mod * b % mod; return t * t % mod; } int num_cases, num_nodes, num_A, num_B; bool marked[1005], vis[1005]; vector<int> connections[1005]; unordered_set<int> A, B; int main() { scanf("%d", &num_cases); for (int t = 0; t < num_cases; t++) { scanf(" %d", &num_nodes); for (int i = 1; i <= num_nodes; i++) connections[i].clear(); for (int i = 0; i < num_nodes - 1; i++) { int a, b; scanf(" %d %d", &a, &b); connections[a].push_back(b); connections[b].push_back(a); } scanf(" %d", &num_A); A.clear(), B.clear(); memset(marked, false, sizeof marked); for (int i = 1; i <= num_A; i++) { int n; scanf(" %d", &n); A.insert(n); marked[n] = true; } scanf(" %d", &num_B); for (int i = 1; i <= num_B; i++) { int n; scanf(" %d", &n); B.insert(n); } int first = *B.begin(); printf("B %d\n", first); fflush(stdout); int ans; scanf(" %d", &ans); if (A.count(ans)) { printf("C %d\n", ans); fflush(stdout); continue; } memset(vis, false, sizeof vis); queue<int> q; q.push(ans); vis[ans] = true; bool done = false; while (!q.empty()) { int node = q.front(); q.pop(); if (marked[node]) { printf("A %d\n", node); fflush(stdout); scanf(" %d", &ans); if (B.count(ans)) { printf("C %d\n", node); done = true; break; } break; } for (int check : connections[node]) { if (!vis[check]) { vis[check] = true; q.push(check); } } } if (!done) printf("C -1\n"); fflush(stdout); } }
#include <bits/stdc++.h> using std::deque; using std::make_pair; using std::map; using std::max; using std::min; using std::pair; using std::set; using std::string; using std::vector; int getCloses(int his, std::vector<int>& mine, std::vector<std::vector<int> >& edges, int gs) { --his; vector<bool> reached(gs, false); static vector<int> process; process.clear(); process.push_back(his); int processIdx = 0; reached[his] = true; while (process.size() > processIdx) { auto x = process[processIdx]; ++processIdx; if (std::find(mine.begin(), mine.end(), x + 1) != mine.end()) { return x + 1; } for (auto y : edges[x]) { if (!reached[y]) { reached[y] = true; process.push_back(y); } } } } int main() { int t; scanf("%d", &t); std::vector<std::vector<int> > g(1000); std::vector<int> mine, his; for (int ddd = 0; ddd < t; ++ddd) { int n; scanf("%d", &n); for (int i = 0; i < n; ++i) { g[i].clear(); } for (int i = 0; i < n - 1; ++i) { int x, y; scanf("%d%d", &x, &y); --x; --y; g[x].push_back(y); g[y].push_back(x); } int ms; scanf("%d", &ms); mine.resize(ms); for (auto& x : mine) { scanf("%d", &x); } scanf("%d", &ms); his.resize(ms); for (auto& x : his) { scanf("%d", &x); } std::cout << "B " << his.front() << std::endl; std::cout.flush(); int ownedByHim; scanf("%d", &ownedByHim); if (std::find(mine.begin(), mine.end(), ownedByHim) != mine.end()) { std::cout << "C " << ownedByHim << std::endl; std::cout.flush(); continue; } int closest = getCloses(ownedByHim, mine, g, n); std::cout << "A " << closest << std::endl; std::cout.flush(); int closesInHim; scanf("%d", &closesInHim); if (std::find(his.begin(), his.end(), closesInHim) != his.end()) { std::cout << "C " << closest << std::endl; std::cout.flush(); } else { std::cout << "C " << -1 << std::endl; std::cout.flush(); } } }
#include <bits/stdc++.h> using namespace std; bool mark[1005]; int main() { int t; cin >> t; while (t--) { int n; cin >> n; vector<vector<int>> adj(n + 1); for (int i = 1, u, v; i < n; ++i) { cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); } memset(mark, 0, sizeof mark); int k1, k2; cin >> k1; vector<int> my(k1); for (auto &i : my) cin >> i, mark[i] = true; cin >> k2; vector<int> ot(k2); for (auto &i : ot) cin >> i; cout << "B " << ot[0] << "\n"; fflush(stdout); int to; cin >> to; int from = my[0]; function<int(int, int)> dfs = [&](int u, int p) { if (u == to) return mark[u] ? u : (1 << 30); int ans = -1; for (auto v : adj[u]) if (v != p) ans = max(ans, dfs(v, u)); if (ans == 1 << 30 && mark[u]) ans = u; return ans; }; int x = dfs(from, -1), a; cout << "A " << x << "\n"; fflush(stdout); cin >> a; bool ok = false; for (auto i : ot) ok |= i == a; if (ok) cout << "C " << x << "\n"; else cout << "C -1\n"; fflush(stdout); } return 0; }
#include <bits/stdc++.h> using namespace std; int T, x, y, n, m, k, v[400000]; bool t[400000]; vector<int> p[400000]; int dfs(int x) { if (v[x] == 2) return x; v[x] = 0; for (auto i : p[x]) if (v[i]) { int r = dfs(i); if (r) return r; } return 0; } int main() { for (scanf("%d", &T); T; T--) { scanf("%d", &n); for (int i = (1); i <= (n); ++i) { p[i].clear(); t[i] = 0; v[i] = 1; } for (int i = (1); i <= (n - 1); ++i) { scanf("%d%d", &x, &y); p[x].push_back(y); p[y].push_back(x); } scanf("%d", &m); for (int i = (1); i <= (m); ++i) { scanf("%d", &x); v[x] = 2; } scanf("%d", &k); for (int i = (1); i <= (k); ++i) { scanf("%d", &x); t[x] = 1; } printf("B %d\n", x); fflush(stdout); scanf("%d", &x); x = dfs(x); printf("A %d\n", x); fflush(stdout); scanf("%d", &y); if (t[y]) printf("C %d\n", x); else printf("C -1\n"); fflush(stdout); } }
#include <bits/stdc++.h> using namespace std; int getInt(); int getNegInt(); int T, N; int get_nearest(int p, int a, vector<vector<int> >& path, unordered_set<int>& me) { if (me.find(a) != me.end()) return a; for (auto b : path[a]) { if (b == p) continue; int tar = get_nearest(a, b, path, me); if (tar != -1) return tar; } return -1; } int main(int argc, char** argv) { int a, b, k1, k2; T = getInt(); while (T--) { unordered_set<int> me, he; N = getInt(); vector<vector<int> > path(N + 1, vector<int>()); for (int i = 1; i < N; i++) { scanf("%d%d", &a, &b); path[a].push_back(b); path[b].push_back(a); } k1 = getInt(); int start; for (int i = 1; i <= k1; i++) { a = getInt(); me.insert(a); } k2 = getInt(); for (int i = 1; i <= k2; i++) { b = getInt(); start = b; he.insert(b); } int ans = -1; for (int i = 1; i <= 1; i++) { cout << "B " << start << endl; fflush(stdout); int index = getInt(); if (me.find(index) != me.end()) { ans = index; break; } int nearest = get_nearest(index, index, path, me); cout << "A " << nearest << endl; fflush(stdout); index = getInt(); if (he.find(index) != he.end()) { ans = nearest; break; } } cout << "C " << ans << endl; fflush(stdout); } return 0; } int getInt() { int ret = 0; char c = getchar(); while (c < '0' || c > '9') c = getchar(); while (c >= '0' && c <= '9') ret *= 10, ret += c - '0', c = getchar(); return ret; } int getNegInt() { int ret = 0, sign = 1; char c = getchar(); while ((c < '0' && c != '-') || c > '9') c = getchar(); if (c == '-') sign = -1, c = getchar(); while (c >= '0' && c <= '9') ret *= 10, ret += c - '0', c = getchar(); return ret * sign; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 100; const int mod = 998244353; int t, n, A[1010], B[1010], vis[1010]; vector<int> adj[1010]; void solve() { cin >> n; for (int i = 1; i < 1010; i++) adj[i].clear(); memset(A, 0, sizeof A); memset(B, 0, sizeof B); memset(vis, 0, sizeof vis); for (int i = 0; i < n - 1; i++) { int a, b; cin >> a >> b; adj[a].push_back(b); adj[b].push_back(a); } int k; cin >> k; for (int i = 0; i < k; i++) { int a; cin >> a; A[a] = true; } cin >> k; for (int i = 0; i < k; i++) { int a; cin >> a; B[a] = true; } for (int i = 1; i <= n; i++) if (B[i]) { cout << "B " << i << endl; break; } int st; cin >> st; queue<int> Q; Q.push(st); while ((int)Q.size()) { int v = Q.front(); Q.pop(); if (A[v]) { cout << "A " << v << endl; cin >> st; if (B[st]) cout << "C " << v << endl; else cout << "C -1" << endl; break; } for (int to : adj[v]) if (!vis[to]) { vis[to] = true; Q.push(to); } } } int main() { ios_base::sync_with_stdio(false), cin.tie(0); cin >> t; while (t--) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> G[1010]; vector<int> label1, label2; int dfs(int v, int parent) { for (auto num : label1) { if (v == num) return v; } for (auto to : G[v]) { if (to == parent) continue; int tmp = dfs(to, v); if (tmp != -1) return tmp; } return -1; } int main(void) { cin.tie(0); ios::sync_with_stdio(false); int t; cin >> t; for (int cnt = 0; cnt < t; cnt++) { for (int i = 0; i < 1010; i++) G[i].clear(); label1.clear(); label2.clear(); int n; cin >> n; for (int i = 0; i < n - 1; i++) { int s, t; cin >> s >> t; G[s].push_back(t); G[t].push_back(s); } int k1; cin >> k1; for (int i = 0; i < k1; i++) { int tmp; cin >> tmp; label1.push_back(tmp); } int k2; cin >> k2; for (int i = 0; i < k2; i++) { int tmp; cin >> tmp; label2.push_back(tmp); } cout << "B " << label2[0] << endl << flush; int v; cin >> v; int s = dfs(v, -1); cout << "A " << dfs(v, -1) << endl << flush; cin >> v; bool find = false; for (auto num : label2) { if (v == num) { cout << "C " << s << endl << flush; find = true; break; } } if (!find) cout << "C -1" << endl << flush; } return 0; }
#include <bits/stdc++.h> using namespace std; int n; int size1; int size2; int myNodes[1000]; int liNodes[1000]; vector<int> graph[1000]; int makeQuery(char s, int n) { int v; printf("%c %d\n", s, n); fflush(stdout); scanf("%d", &v); if (v == -1) exit(0); return v; } int BFS(int p1) { pair<int, int> node1; set<int> visited; queue<pair<int, int> > toVisit; toVisit.push({p1, 1}); visited.insert(p1); while (!toVisit.empty()) { node1 = toVisit.front(); toVisit.pop(); if (node1.second > size2) return -1; for (int node2 : graph[node1.first - 1]) { if (visited.insert(node2).second) { if (binary_search(myNodes, (myNodes + size1), node2)) return node2; toVisit.push({node2, node1.second + 1}); } } } return -1; } int getCommonNode() { int v1; int v2; sort(myNodes, (myNodes + size1)); sort(liNodes, (liNodes + size2)); v1 = makeQuery('B', liNodes[0]); if (binary_search(myNodes, (myNodes + size1), v1)) return v1; v1 = BFS(v1); if (v1 == -1) return -1; v2 = makeQuery('A', v1); if (binary_search(liNodes, (liNodes + size2), v2)) return v1; return -1; } int main() { int t; int n; int v1; int v2; scanf("%d", &t); for (int i = 0; i < t; i++) { scanf("%d", &n); for (int j = 0; j < n; j++) graph[j].clear(); for (int j = 0; j < (n - 1); j++) { scanf("%d", &v1); scanf("%d", &v2); graph[v1 - 1].push_back(v2); graph[v2 - 1].push_back(v1); } scanf("%d", &size1); for (int j = 0; j < size1; j++) scanf("%d", &myNodes[j]); scanf("%d", &size2); for (int j = 0; j < size2; j++) scanf("%d", &liNodes[j]); printf("C %d\n", getCommonNode()); fflush(stdout); } }
#include <bits/stdc++.h> using namespace std; const long long N = 200000; long long t, n, k1, k2, dis[N], ans, anns; vector<long long> g[N]; set<long long> a, b; void dfs(long long v, long long par) { if (a.find(v) != a.end() and dis[v] <= anns) { anns = dis[v]; ans = v; } for (long long i = 0; i < g[v].size(); i++) { long long u = g[v][i]; if (u == par) continue; dis[u] = dis[v] + 1; dfs(u, v); } } int main() { cin >> t; while (t--) { for (long long i = 0; i < 1331; i++) { g[i].clear(); dis[i] = 0; } cin >> n; for (long long i = 1; i < n; i++) { long long u, v; cin >> v >> u; g[v].push_back(u), g[u].push_back(v); } a.clear(); b.clear(); long long now = 0; cin >> k1; for (long long i = 1; i <= k1; i++) { long long p; cin >> p; a.insert(p); } cin >> k2; for (long long i = 1; i <= k2; i++) { long long p; cin >> p; b.insert(p); now = p; } cout << "B " << now << endl; cin >> now; if (a.find(now) != a.end()) { cout << "C " << now << endl; continue; } anns = 1e18; dfs(now, 0); cout << "A " << ans << endl; cin >> now; if (b.find(now) != b.end()) { cout << "C " << ans << endl; continue; } cout << "C -1\n"; } }
#include <bits/stdc++.h> using namespace std; using vi = vector<int>; using vvi = vector<vi>; struct Testcase { set<int> me, him; vvi g; vi near; void dfs(int from, int nearest, int p = -1) { if (me.count(from) != 0) { near[from] = from; } else { near[from] = nearest; } for (int to : g[from]) { if (p == to) continue; dfs(to, near[from], from); } } void solve() { int n; cin >> n; g.assign(n, vi()); near.assign(n, -1); for (int i = 0; i < n - 1; ++i) { int x, y; cin >> x >> y; x--, y--; g[x].push_back(y); g[y].push_back(x); } int k1, k2; cin >> k1; for (int i = 0; i < k1; ++i) { int x; cin >> x; me.insert(x - 1); } cin >> k2; for (int i = 0; i < k2; ++i) { int x; cin >> x; him.insert(x); } auto root = *me.begin(); dfs(root, root); auto y1 = *him.begin(); cout << "B " << y1 << endl; cout << flush; int x1; cin >> x1; if (me.count(x1 - 1) == 1) { cout << "C " << x1 << endl; cout << flush; return; } int x2 = near[x1 - 1] + 1; cout << "A " << x2 << endl; cout << flush; int y2; cin >> y2; if (him.count(y2) == 1) { cout << "C " << x2 << endl; cout << flush; } else { cout << "C -1" << endl; cout << flush; } } }; int main() { int t; cin >> t; while (t--) { Testcase().solve(); cerr << "SOLVED" << endl; } }
#include <bits/stdc++.h> using namespace std; int n; int size1; int size2; int myNodes[1000]; int liNodes[1000]; vector<int> graph[1000]; int makeQuery(char s, int n) { int v; printf("%c %d\n", s, n); fflush(stdout); scanf("%d", &v); if (v == -1) exit(0); return v; } int BFS(int p1) { pair<int, int> node1; set<int> visited; queue<pair<int, int> > toVisit; toVisit.push({p1, 1}); visited.insert(p1); while (!toVisit.empty()) { node1 = toVisit.front(); toVisit.pop(); if (node1.second > size2) return -1; for (int node2 : graph[node1.first - 1]) { if (visited.insert(node2).second) { if (binary_search(myNodes, (myNodes + size1), node2)) return node2; toVisit.push({node2, node1.second + 1}); } } } return -1; } int getCommonNode() { int v1; int v2; sort(myNodes, (myNodes + size1)); sort(liNodes, (liNodes + size2)); v1 = makeQuery('B', liNodes[0]); if (binary_search(myNodes, (myNodes + size1), v1)) return v1; v1 = BFS(v1); if (v1 == -1) return -1; v2 = makeQuery('A', v1); if (binary_search(liNodes, (liNodes + size2), v2)) return v1; return -1; } int main() { int t; int n; int v1; int v2; scanf("%d", &t); for (int i = 0; i < t; i++) { scanf("%d", &n); for (int j = 0; j < n; j++) graph[j].clear(); for (int j = 0; j < (n - 1); j++) { scanf("%d", &v1); scanf("%d", &v2); graph[v1 - 1].push_back(v2); graph[v2 - 1].push_back(v1); } scanf("%d", &size1); for (int j = 0; j < size1; j++) scanf("%d", &myNodes[j]); scanf("%d", &size2); for (int j = 0; j < size2; j++) scanf("%d", &liNodes[j]); printf("C %d\n", getCommonNode()); fflush(stdout); } }
#include <bits/stdc++.h> using namespace std; template <class T> void read(T& x) { cin >> x; } template <class H, class... T> void read(H& h, T&... t) { read(h); read(t...); } template <class A> void read(A* x, int size) { for (int i = (0); (1) > 0 ? i < (size) : i > (size); i += (1)) read(x[i]); } template <class A> void read(vector<A>& x) { for (auto& a : x) read(a); } template <class T> void print(T& x) { cout << x << ' '; } template <class H, class... T> void print(H h, T... t) { print(h); print(t...); } template <class A> void print(A* x, int size) { for (int i = (0); (1) > 0 ? i < (size) : i > (size); i += (1)) print(x[i]); cout << '\n'; } template <class A> void print(vector<A>& x) { for (auto& a : x) print(a); } template <class H, class... T> void debug(H h, T... t) { print(h, t...); cout << endl; } const int d4i[4] = {-1, 0, 1, 0}, d4j[4] = {0, 1, 0, -1}; const int d8i[8] = {-1, -1, 0, 1, 1, 1, 0, -1}, d8j[8] = {0, 1, 1, 1, 0, -1, -1, -1}; const int N = 1010, mod = 1e9 + 7; vector<vector<int>> g; int n; unordered_set<int> st1, st2; int dfs(int s, int p, int u) { if (s == u) return s; int ans = -1; for (int v : g[s]) { if (v != p) { int x = dfs(v, s, u); if (x == -1) continue; ans = x; } } if (ans == -1) return -1; if (st1.find(ans) != st1.end()) return ans; return s; } void solve() { read(n); int u, v, k1, k2; g.clear(); st1.clear(); st2.clear(); g.resize(n + 1); for (int i = (0); (1) > 0 ? i < (n - 1) : i > (n - 1); i += (1)) { read(u, v); g[u].push_back(v); g[v].push_back(u); } read(k1); for (int i = (0); (1) > 0 ? i < (k1) : i > (k1); i += (1)) { read(u); st1.insert(u); } read(k2); for (int i = (0); (1) > 0 ? i < (k2) : i > (k2); i += (1)) { read(u); st2.insert(u); } cout << "A " << (*st1.begin()) << endl; cin >> u; if (st2.find(u) != st2.end()) { cout << "C " << (*st1.begin()) << endl; return; } cout << "B " << (*st2.begin()) << endl; cin >> u; if (st1.find(u) != st1.end()) { cout << "C " << u << endl; return; } u = dfs(*(st1.begin()), 0, u); int x = u; cout << "A " << u << endl; cin >> u; if (st2.find(u) != st2.end()) cout << "C " << x << endl; else cout << "C " << -1 << endl; } signed main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int _t; cin >> _t; while (_t--) solve(); }
#include <bits/stdc++.h> using namespace std; int ask(string q, int x) { cout << q << " " << x << endl; int ret; cin >> ret; return ret; } int getclosestnode(vector<vector<int>> &adj, set<int> &me, int node) { bool visited[1001]; memset(visited, 0, sizeof visited); queue<int> q; q.push(node); while (!q.empty()) { int u = q.front(); q.pop(); if (me.count(u) != 0) return u; else for (auto x : adj[u]) if (!visited[x]) { q.push(x); visited[x] = 1; } } return -1; } void solve() { int n; vector<vector<int>> adj(1001); cin >> n; for (int i = 0; i < (int)(n - 1); i++) { int a, b; cin >> a >> b; adj[a].push_back(b); adj[b].push_back(a); } set<int> me, li; int k; cin >> k; for (int i = 0; i < (int)(k); i++) { int a; cin >> a; me.insert(a); } cin >> k; for (int i = 0; i < (int)(k); i++) { int a; cin >> a; li.insert(a); } int node = ask("B", *li.begin()); if (me.count(node) != 0) cout << "C " << node << endl; else { int closest = getclosestnode(adj, me, node); int liclose = ask("A", closest); if (li.count(liclose) != 0) { cout << "C " << closest << endl; } else cout << "C " << -1 << endl; } } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); int tc; cin >> tc; for (int i = 0; i < (int)(tc); i++) solve(); return 0; }
#include <bits/stdc++.h> using namespace std; vector<vector<int> > e; int d[1000], pr[1000]; void DFS(int x, int p, int dp) { d[x] = dp; pr[x] = p; for (int i = 0; i < e[x].size(); i++) if (e[x][i] != p) DFS(e[x][i], x, dp + 1); } int main() { int t; cin >> t; for (int i = 0; i < t; i++) { int n, a, b, k1, k2, ba[1000] = {}, c[1000] = {}, mn = 1001, ind = -1, x, y; cin >> n; e.resize(n); for (int j = 0; j < n; j++) e[j].clear(); for (int j = 0; j < n - 1; j++) { cin >> a >> b; a--; b--; e[a].push_back(b); e[b].push_back(a); } DFS(0, -1, 0); cin >> k1; for (int j = 0; j < k1; j++) { cin >> x; ba[x - 1] = 1; } cin >> k2; for (int j = 0; j < k2; j++) { cin >> x; c[x - 1] = 1; } for (int j = 0; j < n; j++) if (ba[j] && d[j] < mn) { mn = d[j]; ind = j; } cout << "B " << x << endl; cin >> x; x--; if (ba[x]) { cout << "C " << x + 1 << endl; continue; } while (x >= 0 && !ba[x]) x = pr[x]; if (x >= 0) { cout << "A " << x + 1 << endl; cin >> y; y--; if (c[y]) cout << "C " << x + 1 << endl; else cout << "C -1" << endl; continue; } cout << "A " << ind + 1 << endl; cin >> y; y--; if (c[y]) cout << "C " << ind + 1 << endl; else cout << "C -1" << endl; } }
#include <bits/stdc++.h> using namespace std; const int maxn = 1000 + 1; int T, n, mark1[maxn], mark2[maxn], k, q, ch, w; vector<int> e[maxn]; void dfs(int v, int p) { if (mark1[v] == 1 && ch == 0) { ch = v; } for (auto u : e[v]) { if (u != p) { dfs(u, v); } } return; } int main() { ios::sync_with_stdio(false); cin.tie(0); cin >> T; for (int i = 1; i <= T; i++) { for (int i = 1; i < maxn; i++) { e[i].clear(); mark1[i] = 0; mark2[i] = 0; } cin >> n; for (int i = 1; i < n; i++) { int tmp1, tmp2; cin >> tmp1 >> tmp2; e[tmp1].push_back(tmp2); e[tmp2].push_back(tmp1); } cin >> k; for (int i = 1; i <= k; i++) { int tmp1; cin >> tmp1; mark1[tmp1] = 1; } cin >> k; for (int i = 1; i <= k; i++) { int tmp1; cin >> tmp1; q = tmp1; mark2[tmp1] = 1; } cout << "B " << q << endl; cout << flush; cin >> w; ch = 0; dfs(w, 0); cout << "A " << ch << endl; cout << flush; cin >> w; if (mark2[w] == 1) { cout << "C " << ch << endl; } else { cout << "C " << -1 << endl; } cout << flush; } return 0; }
#include <bits/stdc++.h> using namespace std; const long long int M = 2e5 + 10; const long long int mod = 1e9 + 7; const long long int infi = LLONG_MAX; long long int ans, k, n, x, y, m, mymax = LLONG_MIN, mymin = LLONG_MAX, b, c, z, sum; vector<long long int> v[M]; vector<long long int> vx, vy; set<long long int> sx, sy; long long int query(long long int node, long long int type) { if (type == 1) { cout << "A " << node << endl; } else cout << "B " << node << endl; long long int val; cin >> val; return val; } long long int dfs(long long int node, long long int parent, long long int target) { long long int curr_dist = n; if (node == target) { return 0; } for (auto kk : v[node]) { if (kk != parent) { curr_dist = min(1 + dfs(kk, node, target), curr_dist); } } return curr_dist; } long long int dist(long long int node1, long long int node2) { return dfs(node1, node1, node2); } void solve() { long long int i, j; cin >> n; for (i = 1; i < n + 1; i++) v[i].clear(); for (i = 1; i < n; i++) { cin >> x >> y; v[x].push_back(y); v[y].push_back(x); } vx.clear(); vy.clear(); sx.clear(); sy.clear(); cin >> k; for (i = 1; i < k + 1; i++) { cin >> x; vx.push_back(x); sx.insert(x); } cin >> k; for (i = 1; i < k + 1; i++) { cin >> x; vy.push_back(x); sy.insert(x); } long long int node_in_x = query(vy[0], 2); if (sx.find(node_in_x) != sx.end()) { cout << "C " << node_in_x << endl; return; } long long int curr_node = -1, min_dist = n; for (auto node : vx) { long long int curr_dist = dist(node, node_in_x); if (curr_dist < min_dist) { min_dist = curr_dist; curr_node = node; } } long long int node_in_y = query(curr_node, 1); if (sy.find(node_in_y) != sy.end()) { cout << "C " << curr_node << endl; } else { cout << "C -1" << endl; } } int main() { long long int i, t, j; cin.tie(NULL); cin >> t; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> g[1005]; int x[1005], y[1005]; int t, n, i, u, v, m, ans, tp; void dfs(int u, int fa) { if (x[u]) { cout << "A " << u << endl; fflush(stdout); cin >> tp; if (y[tp]) ans = u; else ans = -1; return; } for (int i = 0; i < g[u].size(); i++) { int v = g[u][i]; if (v == fa) continue; dfs(v, u); if (ans) return; } } int main() { cin >> t; while (t--) { cin >> n; for (i = 1; i <= n; i++) { g[i].clear(); x[i] = y[i] = 0; } for (i = 0; i < n - 1; i++) { cin >> u >> v; g[u].push_back(v); g[v].push_back(u); } cin >> m; for (i = 0; i < m; i++) { cin >> u; x[u] = 1; } cin >> m; for (i = 0; i < m; i++) { cin >> u; y[u] = 1; } cout << "B " << u << endl; fflush(stdout); cin >> u; ans = 0; dfs(u, 0); cout << "C " << ans << endl; fflush(stdout); } }
#include <bits/stdc++.h> using namespace std; int n, k1, k2, u[1001], q[1001], start, x, y; vector<int> vec[1001]; int a, b; int f(int v, int pr) { if (u[v] == 1) { return v; } int yy = 0; for (int i = 0; i < vec[v].size(); i++) { if (vec[v][i] != pr) { yy = max(yy, f(vec[v][i], v)); } } return yy; } pair<int, int> get(int v, int pr) { pair<int, int> ans = make_pair(0, 0); if (v == y) { ans.first = 1; return ans; } if (u[v] == 1) { ans.second = v; } pair<int, int> yy = make_pair(0, 0); for (int i = 0; i < vec[v].size(); i++) { if (vec[v][i] != pr) { yy = max(yy, get(vec[v][i], v)); } } if (yy.first != 0) { ans.first = 1; } if (yy.first != 0 && yy.second != 0) { ans = yy; } return ans; } void solve() { for (int i = 0; i < 1001; i++) { vec[i].clear(); u[i] = 0; q[i] = 0; } cin >> n; for (int i = 1; i < n; i++) { scanf("%d%d", &a, &b); vec[a].push_back(b); vec[b].push_back(a); } cin >> k1; for (int i = 0; i < k1; i++) { scanf("%d", &x); u[x] = 1; } cin >> k2; for (int i = 0; i < k2; i++) { scanf("%d", &x); q[x] = 1; } start = f(1, -1); cout << "A " << start << endl; fflush(stdout); cin >> y; if (q[y] == 1) { cout << "C " << start << endl; fflush(stdout); return; } else { cout << "B " << x << endl; fflush(stdout); cin >> y; if (u[y] == 1) { cout << "C " << y << endl; fflush(stdout); return; } else { pair<int, int> ppp = get(1, -1); if (ppp.second == 0) { cout << "C -1" << endl; fflush(stdout); return; } start = ppp.second; cout << "A " << start << endl; fflush(stdout); cin >> y; if (q[y] == 1) { cout << "C " << start << endl; fflush(stdout); return; } else { cout << "C -1" << endl; fflush(stdout); return; } } } } int main() { int test; cin >> test; while (test--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<vector<int>> graph; vector<bool> used; set<int> tree1; set<int> tree2; int dfs(int u) { if (used[u]) { return 0; } used[u] = true; if (tree1.find(u) != tree1.end()) { return u; } for (int x : graph[u]) { int k = dfs(x); if (k != 0) { return k; } } return 0; } int main() { ios::sync_with_stdio(0); int t; cin >> t; for (int i = 0; i < t; i++) { int n; cin >> n; graph.assign(n + 1, vector<int>(0)); used.assign(n + 1, false); tree1.clear(); tree2.clear(); for (int i = 0; i < n - 1; i++) { int u, v; cin >> u >> v; graph[u].push_back(v); graph[v].push_back(u); } int k1; cin >> k1; for (int i = 0; i < k1; i++) { int u; cin >> u; tree1.insert(u); } int k2; cin >> k2; for (int i = 0; i < k2; i++) { int u; cin >> u; tree2.insert(u); } cout << "B " << *tree2.begin() << endl; int x; cin >> x; int t1 = dfs(x); cout << "A " << t1 << endl; int y; cin >> y; if (tree2.find(y) != tree2.end()) { cout << "C " << t1 << endl; } else { cout << "C " << -1 << endl; } } return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 1e5 + 10; const int K = 200; const int mod = 998244353; int power(int a, int b) { int res = 1; while (b) { if (b & 1) { res = 1LL * res * a % mod; } a = 1LL * a * a % mod; b >>= 1; } return res; } vector<int> adj[1005]; int par[1005]; void dfs(int node, int p) { par[node] = p; for (auto child : adj[node]) { if (child == p) continue; dfs(child, node); } } int main() { int test, n, u, v, k1, k2, val; scanf("%d", &test); while (test--) { set<int> s1, s2; scanf("%d", &n); for (int i = 1; i <= n; i++) { adj[i].clear(); par[i] = -1; } for (int i = 1; i < n; i++) { scanf("%d %d", &u, &v); adj[u].push_back(v); adj[v].push_back(u); } scanf("%d", &k1); for (int i = 1; i <= k1; i++) { scanf("%d", &val); s1.insert(val); } scanf("%d", &k2); for (int i = 1; i <= k2; i++) { scanf("%d", &val); s2.insert(val); } int a1 = *s1.begin(), a2, b1, b2; printf("A %d\n", a1); fflush(stdout); scanf("%d", &b1); if (s2.find(b1) != s2.end()) { printf("C %d\n", a1); fflush(stdout); continue; } b2 = *s2.begin(); printf("B %d\n", b2); fflush(stdout); scanf("%d", &a2); if (s1.find(a2) != s1.end()) { printf("C %d\n", a2); fflush(stdout); continue; } dfs(a1, 0); while (a2) { if (s1.find(a2) != s1.end()) { break; } a2 = par[a2]; } if (a2) { printf("A %d\n", a2); fflush(stdout); scanf("%d", &b2); if (s2.find(b2) != s2.end()) { printf("C %d\n", a2); fflush(stdout); continue; } } printf("C -1\n"); fflush(stdout); } return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1007; const int inf = INT_MAX; const long long inff = 1e18; const long long mod = 1e9 + 7; int t; int n; vector<int> G[maxn]; vector<int> a, b; int ret, nnow = 0; int dfs(int now, int p) { if (now == ret) return 1; int rr = 0; for (int i : G[now]) { if (i != p) { rr = max(rr, dfs(i, now)); } } if (rr == 1 && lower_bound((a).begin(), (a).end(), now) != a.end() && (*lower_bound((a).begin(), (a).end(), now)) == now && nnow == 0) { nnow = now; } return rr; } int32_t main() { ios::sync_with_stdio(0); cin.tie(0); cout.tie(0); cin >> t; while (t--) { cin >> n; for (int i = 1; i <= 1000; i++) G[i].clear(); a.clear(); b.clear(); nnow = 0; ret = 0; for (int i = 1; i <= n - 1; i++) { int x, y; cin >> x >> y; G[x].push_back(y); G[y].push_back(x); } int x; int A, B; cin >> A; while (A--) { cin >> x; a.push_back(x); } sort((a).begin(), (a).end()); cin >> B; while (B--) { cin >> x; b.push_back(x); } sort((b).begin(), (b).end()); cout << "B " << b[0] << endl; cout << flush; cin >> ret; if (lower_bound((a).begin(), (a).end(), ret) != a.end() && (*lower_bound((a).begin(), (a).end(), ret)) == ret) { cout << "C " << ret << endl; cout << flush; } else { dfs(a[0], -1); cout << "A " << nnow << endl; cout << flush; cin >> ret; if (lower_bound((b).begin(), (b).end(), ret) != b.end() && (*lower_bound((b).begin(), (b).end(), ret)) == ret) { cout << "C " << nnow << endl; cout << flush; } else { cout << "C " << -1 << endl; cout << flush; } } } }
#include <bits/stdc++.h> using namespace std; const long long MOD = 1000000007ll; long long powmod(long long a, long long b) { long long res = 1; a %= MOD; assert(b >= 0); for (; b; b >>= 1) { if (b & 1) res = res * a % MOD; a = a * a % MOD; } return res; } template <typename t1, typename t2> inline bool upmax(t1 &a, t2 b) { if (a < (t1)b) { a = (t1)b; return true; } else return false; } template <typename t1, typename t2> inline bool upmin(t1 &a, t2 b) { if (a > (t1)b) { a = (t1)b; return true; } else return false; } template <typename T> inline T gcd(T a, T b) { return b ? gcd(b, a % b) : a; } template <typename T> inline T lcm(T a, T b) { return a * (b / gcd(a, b)); } template <typename T> inline T sqr(T a) { return a * a; } int dx[] = {1, 0, -1, 0, 1, 1, -1, -1}; int dy[] = {0, 1, 0, -1, 1, -1, 1, -1}; const int INF = 1000000404; const long long LINF = 4000000000000000404ll; const long double PI = acos(-1.0); const long double EPS = 1e-9; int SQ = 318; int timer = 0; const int N = 1100; int a[N]; int b[N]; int col[N]; int col2[N]; int d[N]; void solve() { vector<int> g[N]; int n; cin >> n; for (int i = 1; i < n; i++) { int a, b; cin >> a >> b; g[a].push_back(b); g[b].push_back(a); } for (int i = 1; i <= n; i++) { col[i] = 0; col2[i] = 0; d[i] = INF; } int k1, k2; cin >> k1; for (int i = 0; i < k1; i++) { cin >> a[i]; col[a[i]] = 1; } cin >> k2; for (int i = 0; i < k2; i++) { cin >> b[i]; col2[b[i]] = 1; } cout << "B " << b[0] << endl; int v; cin >> v; queue<int> q; d[v] = 0; q.push(v); while (!q.empty()) { int x = q.front(); q.pop(); for (auto y : g[x]) { if (d[y] > d[x] + 1) { d[y] = d[x] + 1; q.push(y); } } } int x = a[0]; for (int i = 0; i < k1; i++) { if (d[a[i]] < d[x]) x = a[i]; } cout << "A " << x << endl; int r; cin >> r; if (col2[r]) { cout << "C " << x << endl; } else { cout << "C " << -1 << endl; } } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); int t = 1; cin >> t; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> using namespace std; template <typename Arg1> void __f(const char* name, Arg1&& arg1) { cerr << name << " : " << arg1 << endl; } template <typename Arg1, typename... Args> void __f(const char* names, Arg1&& arg1, Args&&... args) { const char* comma = strchr(names + 1, ','); cerr.write(names, comma - names) << " : " << arg1 << " | "; __f(comma + 1, args...); } float inf = std::numeric_limits<double>::infinity(); long long int INF = std::numeric_limits<long long int>::max(); const int N = 1005; set<int> X, Y; vector<int> G[N]; int dfs(int x, int pre) { if (X.count(x)) return x; int ret; for (auto v : G[x]) { if (v == pre) continue; ret = dfs(v, x); if (ret) return ret; } return 0; } int getinput() { int x; cin >> x; if (x == -1) exit(0); return x; } int main() { int t; cin >> t; ; while (t--) { int n; n = getinput(); for (int i = 1; i <= n; i++) G[i].clear(); X.clear(), Y.clear(); int a, b; for (int i = 1; i < n; i++) { cin >> a >> b; G[a].push_back(b); G[b].push_back(a); } int k1, k2, v; cin >> k1; for (int i = 0; i < k1; i++) cin >> v, X.insert(v); cin >> k2; for (int i = 0; i < k2; i++) cin >> v, Y.insert(v); cout << "B " << *(Y.begin()) << endl; cout.flush(); int x1, x2, y2; x1 = getinput(); x2 = dfs(x1, 0); cout << "A " << x2 << endl; cout.flush(); y2 = getinput(); if (Y.count(y2)) cout << "C " << x2 << endl; else cout << "C -1" << endl; cout.flush(); } return 0; }
#include <bits/stdc++.h> using namespace std; const int inf = 0x3f3f3f3f; const long long INF = 0x3f3f3f3f3f3f3f3fLL; const double pi = acos(-1.0); const int maxn = 100000 + 10; const int mod = 1e9 + 7; inline char _getchar() { static const int BUFSIZE = 100001; static char buf[BUFSIZE]; static char *psta = buf, *pend = buf; if (psta >= pend) { psta = buf; pend = buf + fread(buf, 1, BUFSIZE, stdin); if (psta >= pend) return -1; } return *psta++; } void dfs(int x, int fa, vector<vector<int> > &g, vector<int> &p, vector<int> &vis) { for (int i = 0; i < g[x].size(); i++) { if (g[x][i] != fa && !vis[g[x][i]]) { p[g[x][i]] = p[x]; dfs(g[x][i], x, g, p, vis); } } } void gao(int n) { vector<vector<int> > g; vector<int> p; vector<int> vis; g.resize(n + 2); p.resize(n + 2); vis.resize(n + 2); for (int i = 1; i < n; i++) { int u, v; scanf("%d", &u), scanf("%d", &v); g[u].push_back(v), g[v].push_back(u); } int k1; scanf("%d", &k1); for (int i = 0; i < k1; i++) { int u; scanf("%d", &u); vis[u] = 1; p[u] = u; } for (int i = 1; i <= n; i++) { if (vis[i]) dfs(i, 0, g, p, vis); } int k2; scanf("%d", &k2); vector<int> q(k2); for (int i = 0; i < k2; i++) { scanf("%d", &q[i]); } sort(q.begin(), q.end()); printf("B %d\n", q[0]); fflush(stdout); int id; scanf("%d", &id); printf("A %d\n", p[id]); fflush(stdout); int ret; scanf("%d", &ret); int w = lower_bound(q.begin(), q.end(), ret) - q.begin(); if (w != q.size() && q[w] == ret) printf("C %d\n", p[id]), fflush(stdout); else printf("C -1\n"), fflush(stdout); } int main() { int T; scanf("%d", &T); for (int cas = 1; cas <= T; cas++) { int n; scanf("%d", &n); gao(n); } return 0; }
#include <bits/stdc++.h> using namespace std; vector<int> adj[1009]; bool visited[1009], vis[1009], has[1009]; int common = -1; void init() { common = -1; for (int i = 0; i < 1009; i++) { visited[i] = false; vis[i] = false; has[i] = false; adj[i].clear(); } } void DFS(int node) { if (common != -1) return; if (visited[node]) { common = node; return; } vis[node] = true; for (int i = 0; i < adj[node].size(); i++) { if (!vis[adj[node][i]]) DFS(adj[node][i]); } } int main() { int test; cin >> test; while (test--) { init(); int n; cin >> n; for (int i = 0; i < n - 1; i++) { int u, v; cin >> u >> v; adj[u].push_back(v); adj[v].push_back(u); } int k1; cin >> k1; for (int i = 0; i < k1; i++) { int x; cin >> x; visited[x] = true; } int k2, node; cin >> k2; for (int i = 0; i < k2; i++) { cin >> node; has[node] = true; } cout << "B " << node << "\n"; int res; cin >> res; if (visited[res]) { cout << "C " << res << "\n"; cout.flush(); continue; } DFS(res); cout << "A " << common << "\n"; cin >> res; if (has[res]) cout << "C " << common << "\n"; else cout << "C -1\n"; cout.flush(); } }
#include <bits/stdc++.h> using namespace std; const int MD = 1000000007; const int INF = 1e9 + 9; const int N = 1e3 + 33; long long n, m, k; vector<int> g[N]; int my[N], opp[N]; int mark[N]; int main() { ios_base::sync_with_stdio(false); cout.tie(nullptr); cin.tie(nullptr); int t; cin >> t; while (t--) { cin >> n; for (int i = 0; i < n; i++) { g[i].clear(); mark[i] = 0; my[i] = 0; opp[i] = 0; } for (int i = 1; i < n; i++) { int a, b; cin >> a >> b; g[a - 1].push_back(b - 1); g[b - 1].push_back(a - 1); } cin >> k; while (k--) { int a; cin >> a; my[a - 1] = 1; } cin >> k; int qq; while (k--) { int a; cin >> a; qq = a; opp[a - 1] = 1; } cout << "B " << qq << endl; int x; cin >> x; if (my[x - 1] == 1) { cout << "C " << x << endl; continue; } queue<int> bfsq; bfsq.push(x - 1); while (!bfsq.empty()) { int v = bfsq.front(); mark[v] = 1; bfsq.pop(); for (int u : g[v]) { if (my[u] == 1) { cout << "A " << u + 1 << endl; int y; cin >> y; if (opp[y - 1] == 1) { cout << "C " << u + 1 << endl; break; } else { cout << "C " << -1 << endl; break; } } if (mark[u] == 0) bfsq.push(u); } } } return 0; }
#include <bits/stdc++.h> using namespace std; vector<vector<int>> g; bool istree[1001], istree2[1001]; vector<int> tr1, tr2; int dfs(int u, int p) { if (istree[u]) { cout << "A " << u + 1 << endl; int q; cin >> q; if (istree2[q - 1]) return u + 1; return -1; } for (int i = 0; i < g[u].size(); ++i) { if (g[u][i] == p) continue; int x = dfs(g[u][i], u); if (x) return x; } return 0; } int main() { ios::sync_with_stdio(0); cin.tie(0); int T; cin >> T; while (T--) { int n; cin >> n; g.clear(); g.resize(n + 1); tr1.clear(); tr2.clear(); memset(istree, 0, sizeof(istree)); memset(istree2, 0, sizeof(istree2)); for (int i = 0; i < n - 1; ++i) { int a, b; cin >> a >> b; g[--a].push_back(--b); g[b].push_back(a); } int k; cin >> k; for (int i = 0; i < k; ++i) { int x; cin >> x; istree[--x] = 1; tr1.push_back(x); } cin >> k; for (int i = 0; i < k; ++i) { int x; cin >> x; istree2[--x] = 1; tr2.push_back(x); } cout << "B " << tr2[0] + 1 << endl; int q; cin >> q; cout << "C " << dfs(q - 1, -1) << endl; } return 0; }
#include <bits/stdc++.h> using namespace std; vector<long long> adj[300001]; set<long long> my, his; long long dfs(long long x, long long p) { long long i, ch, k; if (my.find(x) != my.end()) { return x; } for (i = 0; i < adj[x].size(); i++) { ch = adj[x][i]; if (ch != p) { k = dfs(ch, x); if (k != 0) return k; } } return 0; } int main() { long long m, z, i, j, lt, x, y, d, r, q, k, g, t, n; vector<long long> a(300001), b(300001), c(300001), tx, ps; ios_base::sync_with_stdio(false); cin.tie(NULL); cout.tie(NULL); cin >> t; while (t--) { cin >> n; for (i = 1; i <= n; i++) adj[i].clear(); my.clear(); his.clear(); for (i = 1; i < n; i++) { cin >> x >> y; adj[x].push_back(y); adj[y].push_back(x); } long long km, kh; cin >> km; for (i = 0; i < km; i++) { cin >> x; my.insert(x); } cin >> kh; for (i = 0; i < kh; i++) { cin >> x; his.insert(x); } cout << "B " << x << endl; cin >> x; if (my.find(x) != my.end()) { cout << "C " << x << endl; continue; } k = dfs(x, 0); if (k == 0) cout << -1 << endl; else { cout << "A " << k << endl; cin >> x; if (his.find(x) != his.end()) cout << "C " << k << endl; else cout << "C -1" << endl; } } }
#include <bits/stdc++.h> using namespace std; template <class T, class R> istream& operator>>(istream& in, pair<T, R>& p) { in >> p.first >> p.second; return in; } template <class T> istream& operator>>(istream& in, vector<T>& v) { for (auto& x : v) { in >> x; } return in; } const long long int mx = 210005; vector<long long int> a, b, v; vector<vector<long long int> > g; long long int n, k1, k2; long long int findClosest(const long long int& x) { v[x] = 1; if (a[x]) { return x; } for (const auto& nx : g[x]) { if (!v[nx]) { int vl; if ((vl = findClosest(nx)) != -1) { return vl; } } } return -1; } void read(long long int& x) { cin >> x; x--; } void print(const char& c, const long long int& x) { cout << c << " " << x + 1 << endl; cout.flush(); } void testcase() { cin >> n; g.clear(); g.resize(n, vector<long long int>()); a.clear(); a.resize(n, 0); b.clear(); b.resize(n, 0); v.clear(); v.resize(n, 0); for (long long int i = 0; i < (n - 1); i++) { long long int x, y; read(x); read(y); g[x].push_back(y); g[y].push_back(x); } cin >> k1; for (long long int i = 0; i < (k1); i++) { long long int x; read(x); a[x] = 1; } cin >> k2; long long int nd2, nd1; for (long long int i = 0; i < (k2); i++) { long long int x; read(x); b[x] = 1; nd2 = x; } print('B', nd2); read(nd1); nd1 = findClosest(nd1); print('A', nd1); read(nd2); if (b[nd2]) { print('C', nd1); } else { cout << "C -1\n"; cout.flush(); } return; } int main() { ios_base::sync_with_stdio(0); long long int t; cin >> t; while (t--) { testcase(); } return 0; }
#include <bits/stdc++.h> using namespace std; int t, n; vector<int> graph[1005]; bool st1[1005], st2[1005]; bool visited[1005]; bool finished; void dfs(int node) { if (st1[node]) { cout << "A " << node << "\n"; int node1; cin >> node1; cout << "C "; if (st2[node1]) { cout << node << "\n"; } else { cout << -1 << "\n"; } finished = true; cout.flush(); return; } visited[node] = true; for (auto c : graph[node]) { if (!visited[c]) { dfs(c); if (finished) { return; } } } } int main() { cin >> t; while (t--) { for (int i = 1; i <= n; ++i) { graph[i].clear(); st1[i] = false; st2[i] = false; visited[i] = false; finished = false; } cin >> n; for (int i = 0; i < n - 1; ++i) { int u, v; cin >> u >> v; graph[u].push_back(v); graph[v].push_back(u); } int k1; cin >> k1; for (int i = 0; i < k1; ++i) { int x; cin >> x; st1[x] = true; } int k2; cin >> k2; int s; for (int i = 0; i < k2; ++i) { int x; cin >> x; st2[x] = true; if (i == 0) { s = x; } } cout << "B " << s << "\n"; cin >> s; dfs(s); } return 0; }
#include <bits/stdc++.h> template <typename T1, typename T2> inline void chmin(T1 &a, T2 b) { if (a > b) a = b; } template <typename T1, typename T2> inline void chmax(T1 &a, T2 b) { if (a < b) a = b; } using namespace std; class Solve { public: int n; vector<vector<int>> treeone; vector<int> dist; vector<int> tapu; vector<int> tapi; void input() { cin >> n; treeone.resize(n + 1); for (int i = int(0); i < int(n - 1); i++) { int a, b; cin >> a >> b; treeone[a].push_back(b); treeone[b].push_back(a); } int k; cin >> k; for (int i = int(0); i < int(k); i++) { int tmp; cin >> tmp; tapu.push_back(tmp); } cin >> k; for (int i = int(0); i < int(k); i++) { int tmp; cin >> tmp; tapi.push_back(tmp); } } void query(char c, int n) { cout << c << " " << n << endl; } void bfs(int s) { dist.resize(n + 1, (1 << 30) - 1); queue<int> que; dist[s] = 0; que.push(s); while (!que.empty()) { int top = que.front(); que.pop(); for (auto e : treeone[top]) { int nd = dist[top] + 1; if (dist[e] > nd) { dist[e] = nd; que.push(e); } } } } void solve() { input(); query('B', tapi[0]); int start; cin >> start; bfs(start); int r = -1; int min_dist = (1 << 30) - 1; for (auto e : tapu) { if (dist[e] < min_dist) { r = e; min_dist = dist[e]; } } if (r == -1) { query('C', -1); return; } query('A', r); int tapya; cin >> tapya; if (find(begin(tapi), end(tapi), tapya) != tapi.end()) { query('C', r); } else { query('C', -1); } } }; int main() { int t; cin >> t; while (t--) { Solve().solve(); } return 0; }
#include <bits/stdc++.h> clock_t t_; using namespace std; int main(int argc, const char* argv[]) { t_ = clock(); int t; cin >> t; while (t--) { int n; cin >> n; vector<int> edges[1010]; int a, b; for (int i = int(0); i < int(n - 1); i++) { cin >> a >> b; edges[a].push_back(b); edges[b].push_back(a); } int k1; cin >> k1; set<int> xs; for (int i = int(0); i < int(k1); i++) { cin >> a; xs.insert(a); } int k2; set<int> ys; cin >> k2; for (int i = int(0); i < int(k2); i++) { cin >> a; ys.insert(a); } int resp; cout << "B " << a << endl; cout << flush; cin >> resp; if (xs.find(resp) != xs.end()) { cout << "C " << resp << endl; cout << flush; } else { queue<int> q; vector<int> dist(n + 7, -1); q.push(resp); dist[resp] = 0; while (xs.find(q.front()) == xs.end()) { int fr = q.front(); q.pop(); for (int i = int(0); i < int(edges[fr].size()); i++) { int to = edges[fr][i]; if (dist[to] == -1) { dist[to] = dist[fr] + 1; q.push(to); } } } a = q.front(); cout << "A " << a << endl; cout << flush; cin >> resp; if (ys.find(resp) != ys.end()) { cout << "C " << a << endl; cout << flush; } else { cout << "C " << -1 << endl; cout << flush; } } } t_ = clock() - t_; cerr << setprecision(9) << fixed << ((float)t_ / CLOCKS_PER_SEC) << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int INF = 1e9 + 7, M = 998244353, N = 1e5 + 7; int f[N], inv[N], fi[N]; int INV(int i) { if (i == 1) return 1; return M - (long long)M / i * INV(M % i) % M; } int C(int n, int k) { return (long long)f[n] * fi[k] % M * fi[n - k] % M; } int H(int n, int k) { if (n == 0) return k == 0; return C(n + k - 1, k); } void add(int& a, int b) { a += b; if (a >= M) a -= M; } signed main() { std::ios::sync_with_stdio(0); std::cin.tie(0); ; f[0] = 1; for (int i = 1; i < N; i++) f[i] = (long long)f[i - 1] * i % M; inv[1] = 1; for (int i = 2; i < N; i++) inv[i] = M - (long long)M / i * inv[M % i] % M; fi[0] = 1; for (int i = 1; i < N; i++) fi[i] = (long long)fi[i - 1] * inv[i] % M; int p, s, r; cin >> p >> s >> r; if (p == 1) return cout << 1 << endl, 0; auto go = [&](int score, int cnt, int sum) { if (cnt == 0) return sum ? 0 : 1; if (score == 0) return cnt ? 0 : 1; int ans = 0; for (int illegal = 0; illegal <= cnt; illegal++) { int ways = C(cnt, illegal); int rem_sum = sum - score * illegal; if (rem_sum < 0) continue; ways = (long long)ways * H(cnt, rem_sum) % M; if (illegal & 1) ways = M - ways; add(ans, ways); } return ans; }; int yes = 0, all = 0; for (int score = r; score <= s; score++) { int tot_ways = H(p - 1, s - score); add(all, tot_ways); for (int same = 0; same <= p - 1; same++) { int rem_sum = s - (same + 1) * score, rem_cnt = p - 1 - same; if (rem_sum < 0) continue; int ways = (long long)go(score, rem_cnt, rem_sum) * C(p - 1, same) % M; ways = (long long)ways * inv[same + 1] % M; add(yes, ways); } } int ans = (long long)yes * INV(all) % M; cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; const int64_t MOD = 998244353; void add(int64_t& a, int64_t b) { a = (a + b) % MOD; } void mul(int64_t& a, int64_t b) { a = a * b % MOD; } vector<int64_t> fact, seq_inv, fact_inv; void create_fact_mod(int num) { fact[0] = 1; fact[1] = 1; for (int i = 2; i <= num; i++) { fact[i] = fact[i - 1] * i % MOD; } } void create_seq_inv_mod(int num) { seq_inv[0] = 1; seq_inv[1] = 1; for (int i = 2; i <= num; i++) { seq_inv[i] = (MOD - MOD / i) * seq_inv[MOD % i] % MOD; } } void create_fact_inv_mod(int num) { fact_inv[0] = 1; fact_inv[1] = 1; for (int i = 2; i <= num; i++) { fact_inv[i] = fact_inv[i - 1] * seq_inv[i] % MOD; } } void create_mod_tables(int num) { fact.resize(num + 1); seq_inv.resize(num + 1); fact_inv.resize(num + 1); create_fact_mod(num); create_seq_inv_mod(num); create_fact_inv_mod(num); } int64_t comb_mod(int n, int k) { return fact[n] * fact_inv[n - k] % MOD * fact_inv[k] % MOD; } int64_t perm_mod(int n, int k) { return fact[n] * fact_inv[n - k] % MOD; } int64_t power_mod(int64_t num, int64_t power) { int64_t prod = 1; num %= MOD; while (power > 0) { if (power & 1) prod = prod * num % MOD; num = num * num % MOD; power >>= 1; } return prod; } int64_t extgcd(int64_t a, int64_t b, int64_t& x, int64_t& y) { int64_t d = a; if (b != 0) { d = extgcd(b, a % b, y, x); y -= (a / b) * x; } else { x = 1; y = 0; } return d; } int64_t inv_mod(int64_t a) { int64_t x, y; extgcd(a, MOD, x, y); return (MOD + x % MOD) % MOD; } int P, S, R; int64_t calc(int people, int sum, int limit) { if (people == 0) return (sum == 0 ? 1 : 0); int64_t ret = 0; for (int over = 0; over <= people && over * limit <= sum; over++) { int64_t result = comb_mod(people, over); int64_t rest = sum - over * limit; mul(result, comb_mod(rest + people - 1, people - 1)); add(ret, (over % 2 ? MOD - result : result)); } return ret; } int main() { cin >> P >> S >> R; create_mod_tables(10000); int64_t ans = 0; for (int a = R; a <= S; a++) { for (int b = 1; b <= P && a * b <= S; b++) { int64_t result = comb_mod(P - 1, b - 1) * calc(P - b, S - a * b, a) % MOD; mul(result, inv_mod(b)); add(ans, result); } } mul(ans, inv_mod(comb_mod(S - R + P - 1, P - 1))); cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int C[5500][5500]; class Solution { const int MOD = 998244353; int inv(int x) { return x == 1 ? 1 : 1ll * (MOD - MOD / x) * inv(MOD % x) % MOD; } void init() { for (int i = 0; i < 5500; ++i) { C[i][i] = C[i][0] = 1; for (int j = 1; j < i; ++j) { C[i][j] = C[i - 1][j] + C[i - 1][j - 1]; if (C[i][j] >= MOD) C[i][j] -= MOD; } } } int dp(int p, int s, int m) { if (p == 0) return s == 0; int ans = 0; for (int i = 0; p - 1 + s - i * m >= 0 and i <= p; ++i) { ans += 1ll * C[p - 1 + s - i * m][p - 1] * (i & 1 ? MOD - 1 : 1) % MOD * C[p][i] % MOD; if (ans >= MOD) ans -= MOD; } return ans; } int p, s, r; public: void run(istream &in, ostream &out) { in >> p >> s >> r; if (p == 1) return out << 1 << '\n', void(); init(); long long ans = 0; const int ALL = C[p - 1 + s - r][p - 1]; for (int score = r; score <= s; ++score) { for (int i = 1; i <= p; ++i) { ans += 1ll * inv(i) * C[p - 1][i - 1] % MOD * dp(p - i, s - score * i, score) % MOD; cerr << dp(p - i, s - score * i, score) << '\n'; if (ans >= MOD) ans -= MOD; } } out << 1ll * ans * inv(ALL) % MOD << '\n'; } }; int main() { ios_base::sync_with_stdio(false); cin.tie(0); Solution().run(cin, cout); }
#include <bits/stdc++.h> using namespace std; inline int read() { int x = 0, f = 1; char c = getchar(); while (c < '0' || c > '9') { if (c == '-') f = -1; c = getchar(); } while (c >= '0' && c <= '9') x = (x << 3) + (x << 1) + (c ^ '0'), c = getchar(); return x * f; } const int N = 6e3 + 5, M = 205, mod = 998244353; inline int inc(int x, int y) { x += y - mod; return x + (x >> 31 & mod); } inline int del(int x, int y) { x -= y; return x + (x >> 31 & mod); } inline int mul(int x, int y) { return 1ll * x * y % mod; } inline void Inc(int &x, int y) { x = inc(x, y); } inline void Del(int &x, int y) { x = del(x, y); } inline long long Pow(long long x, int k) { long long res = 1; while (k) { if (k & 1) res = res * x % mod; x = x * x % mod; k >>= 1; } return res; } int c[N][N]; void init(int n, int m) { c[0][0] = 1; for (int i = 1; i <= n; i++) { c[i][0] = 1; for (int j = 1; j <= min(i, m); j++) c[i][j] = inc(c[i - 1][j - 1], c[i - 1][j]); } } inline int C(const int n, const int m) { if (n < m || n < 0 || m < 0) return 0; return c[n][m]; } inline int calc(const int n, const int m, const int x) { if (n == 0) return 1; if (n < 0) return 0; int res = 0; for (int i = 0, k = -1; i <= m; i++) { k *= -1; if (k > 0) Inc(res, mul(C(m, i), C(n - i * x + m - 1, m - 1))); else Del(res, mul(C(m, i), C(n - i * x + m - 1, m - 1))); } return res; } int p, s, r, ans, inv[M]; int main() { p = read(), s = read(), r = read(); init(s + p, 100); for (int i = 1; i <= p; i++) inv[i] = Pow(i, mod - 2); for (int x = r; x <= s; x++) for (int i = 1; i <= p; i++) { if ((p - i) * (x - 1) + i * x < s) continue; Inc(ans, mul(mul(C(p - 1, i - 1), calc(s - i * x, p - i, x)), inv[i])); } printf("%d\n", mul(ans, Pow(C(s - r + p - 1, p - 1), mod - 2))); return 0; }
#include <bits/stdc++.h> std::mt19937 rng( (int)std::chrono::steady_clock::now().time_since_epoch().count()); const int ms = 100100; const long long MOD = 998244353; long long fexp(long long x, long long e = MOD - 2) { long long ans = 1; for (; e > 0; e /= 2) { if (e & 1) ans = ans * x % MOD; x = x * x % MOD; } return ans; } long long inv[ms]; long long fat[ms], ifat[ms]; long long comb(int n, int a) { if (a < 0 || a > n) return 0; else return fat[n] * ifat[a] % MOD * ifat[n - a] % MOD; } long long sum(int S, int K, int m) { if (S == 0 && K == 0) return 1; long long ans = 0; for (int i = 0; i <= K && i * m <= S; i++) { long long cur = comb(S - i * m + K - 1, K - 1) * comb(K, i) % MOD; if (i % 2 == 1) { cur = (MOD - cur) % MOD; } ans = (ans + cur) % MOD; } return ans; } int main() { std::ios_base::sync_with_stdio(false); std::cin.tie(NULL); int p, s, r; std::cin >> p >> s >> r; fat[0] = ifat[0] = 1; for (int i = 1; i < ms; i++) { inv[i] = fexp(i); fat[i] = fat[i - 1] * i % MOD; ifat[i] = ifat[i - 1] * inv[i] % MOD; } long long q = 0; long long ans = 0; for (int v = r; v <= s; v++) { for (int o = 0; o + 1 <= p && v * (o + 1) <= s; o++) { int x = p - (o + 1); if (x > 0 && v == 0) continue; ans = (ans + sum(s - v * (o + 1), x, v) * comb(p - 1, o) % MOD * inv[o + 1]) % MOD; } q = (q + sum(s - v, p - 1, s + 1)) % MOD; } std::cout << ans * fexp(q) % MOD << '\n'; }
#include <bits/stdc++.h> using namespace std; int n, s, r, ans; int inv[10010], fac[10010]; template <typename T> void chkmin(T &x, T y) { x = min(x, y); } template <typename T> void chkmax(T &x, T y) { x = max(x, y); } template <typename T> void read(T &x) { x = 0; int f = 1; char ch = getchar(); while (!isdigit(ch)) { if (ch == '-') f = -1; ch = getchar(); } while (isdigit(ch)) { x = x * 10 + ch - '0'; ch = getchar(); } x *= f; } void update(int &x, int y) { x = (x + y >= 998244353) ? (x + y - 998244353) : (x + y); } int mul(int x, int y) { return 1ll * x * y % 998244353; } int inc(int x, int y) { return (x + y >= 998244353) ? (x + y - 998244353) : (x + y); } int dec(int x, int y) { return (x - y < 0) ? (x - y + 998244353) : (x - y); } int qpow(int a, int b) { int ret = 1; while (b) { if (b & 1) ret = 1ll * ret * a % 998244353; a = 1ll * a * a % 998244353; b >>= 1; } return ret; } void init(int n) { fac[0] = inv[0] = 1; for (int i = 1; i <= n; ++i) fac[i] = mul(fac[i - 1], i); inv[n] = qpow(fac[n], 998244353 - 2); for (int i = n - 1; i >= 1; --i) inv[i] = mul(inv[i + 1], i + 1); } int C(int n, int m) { if (m < 0 || m > n) return 0; return mul(fac[n], mul(inv[m], inv[n - m])); } int calc(int n, int m) { if (n == 0 && m == 0) return 1; return C(n + m - 1, m - 1); } int work(int n, int s, int lim) { if (s < 0) return 0; if (s == 0) return 1; int ret = 0; for (int i = 0; i <= n; ++i) { int tmp = mul(C(n, i), calc(s - i * (lim + 1), n)); if (i & 1) ret = dec(ret, tmp); else ret = inc(ret, tmp); } return ret; } int main() { read(n), read(s), read(r); init(10010 - 2); if (r == 0 && s == 0) update(ans, qpow(n, 998244353 - 2)); for (int i = max(r, 1); i <= s; ++i) for (int j = 1; j <= n; ++j) { int tmp = work(n - j, s - i * j, i - 1); int coef = C(n - 1, j - 1); coef = mul(coef, qpow(j, 998244353 - 2)); update(ans, mul(coef, tmp)); } int tim = 0; for (int i = r; i <= s; ++i) update(tim, calc(s - i, n - 1)); ans = mul(ans, qpow(tim, 998244353 - 2)); printf("%d\n", ans); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 2e5 + 7; const int inf = 0x3f3f3f3f; const long long INF = 0x3f3f3f3f3f3f3f3f; const int mod = 998244353; const double eps = 1e-8; long long comb[5201][5201], p, s, r; long long fastPow(long long a, long long b) { long long ans = 1; while (b) { if (b & 1) ans = ans * a % mod; a = a * a % mod; b >>= 1; } return ans; } long long calc(long long p, long long up, long long sum) { if (p == 0) return sum == 0; long long ans = 0; for (int i = 0; i <= p; i++) { if (i * up > sum) break; if (i & 1) ans = (ans - comb[p][i] * comb[sum - i * up + p - 1][p - 1] % mod + mod) % mod; else ans = (ans + comb[p][i] * comb[sum - i * up + p - 1][p - 1] % mod) % mod; } return ans; } int main() { for (int i = 0; i <= 5200; i++) for (int j = comb[i][0] = 1; j <= i; j++) comb[i][j] = (comb[i - 1][j] + comb[i - 1][j - 1]) % mod; scanf("%lld%lld%lld", &p, &s, &r); if (p == 1) { puts("1"); } else if (s == 0) { printf("%d\n", fastPow(p, mod - 2)); } else { long long Q = 0, P = 0; for (int i = r; i <= s; i++) { Q = (Q + comb[s - i + p - 2][p - 2]) % mod; for (int j = 0; j < p && j * i + i <= s; j++) { long long cnt1 = comb[p - 1][j]; long long cnt2 = calc(p - j - 1, i, s - (j * i + i)); P = (P + cnt1 * cnt2 % mod * fastPow(j + 1, mod - 2) % mod) % mod; } } printf("%lld\n", P * fastPow(Q, mod - 2) % mod); } return 0; }
#include <bits/stdc++.h> #pragma GCC optimize("O2") #pragma GCC optimize("unroll-loops") using namespace std; const long double eps = 1e-7; const int inf = 1000000010; const long long INF = 10000000000000010LL; const int mod = 998244353; const int MAXN = 5110, LOG = 20; long long n, s, r, u, v, x, y, t, a, b, ans; long long F[MAXN], I[MAXN]; long long dp[110]; long long powmod(long long a, long long b) { if (!b) return 1; if (b & 1) return a * powmod(a * a % mod, b >> 1) % mod; return powmod(a * a % mod, b >> 1); } long long C(long long n, long long r) { if (n < 0 || n < r) return 0; return (F[n] * I[r] % mod) * I[n - r] % mod; } long long count(long long k, long long n) { if (!k && !n) return 1; return C(n + k - 1, k - 1); } long long f(long long n, long long sum, long long lim) { long long res = 0; for (int i = 0; i <= n && i * lim <= sum; i++) { long long tmp = count(n, sum - lim * i) * C(n, i) % mod; if (i & 1) tmp = -tmp; res += tmp; } return res % mod; } int main() { ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0); F[0] = 1; for (int i = 1; i < MAXN; i++) F[i] = F[i - 1] * i % mod; I[MAXN - 1] = powmod(F[MAXN - 1], mod - 2); for (int i = MAXN - 1; i; i--) I[i - 1] = I[i] * i % mod; cin >> n >> s >> r; for (int x = r; x <= s; x++) for (int t = 1; t <= n && t * x <= s; t++) ans += C(n, t) * f(n - t, s - t * x, x) % mod; ans %= mod; ans = ans * powmod(C(s - r + n - 1, n - 1), mod - 2) % mod; ans = ans * powmod(n, mod - 2) % mod; cout << ans << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; const long long mod = 998244353; long long p, r, s, ans, fact[6010]; long long winHasMoreThanr, oneHasMoreThanr; long long pw(long long a, long long b) { long long res = 1; while (b) { if (b & 1) { res *= a; res %= mod; } a *= a; a %= mod; b >>= 1; } return res; } void precalc() { fact[0] = fact[1] = 1; for (long long i = 2; i <= 6000; ++i) { fact[i] = fact[i - 1] * i; fact[i] %= mod; } } long long aCb(long long a, long long b) { if (a < b or b < 0) { return 0; } return ((fact[a] * pw((fact[b] * fact[a - b]) % mod, mod - 2)) % mod); } signed main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); precalc(); cin >> p >> s >> r; for (long long i = 1, sgn = 1; i <= p; ++i, sgn *= -1) { winHasMoreThanr += sgn * ((aCb(p, i) * aCb(s - i * r + p - 1, p - 1)) % mod); winHasMoreThanr %= mod; if (winHasMoreThanr < 0) { winHasMoreThanr += mod; } } oneHasMoreThanr = aCb(s - r + p - 1, p - 1); ans = winHasMoreThanr; ans *= pw(p, mod - 2); ans %= mod; ans *= pw(oneHasMoreThanr, mod - 2); ans %= mod; cout << ans; }
#include <bits/stdc++.h> using namespace std; template <typename T> using minpq = priority_queue<T, vector<T>, greater<T>>; template <int m> struct mod { long long x; mod() : x(0) {} mod(long long xx) : x(xx) { if (abs(x) >= m) x %= m; if (x < 0) x += m; } mod operator+(const mod &a) const { mod n; n.x = x + a.x; if (n.x >= m) n.x -= m; return n; } mod operator-(const mod &a) const { mod n; n.x = x - a.x; if (n.x < 0) n.x += m; return n; } mod operator*(const mod &a) const { return x * a.x; } mod operator+=(const mod &a) { x += a.x; if (x >= m) x -= m; return *this; } mod operator-=(const mod &a) { x -= a.x; if (x < 0) x += m; return *this; } mod operator*=(const mod &a) { x = (x * a.x) % m; return *this; } mod pow(long long b) const { mod ans = 1; mod a = *this; while (b > 0) { if (b & 1) ans *= a; a *= a; b /= 2; } return ans; } mod inv() const { return pow(m - 2); } mod operator/(const mod &a) const { return (*this) * a.inv(); } mod operator/=(const mod &a) { return (*this) *= a.inv(); } bool operator==(const mod &o) const { return x == o.x; } bool operator!=(const mod &o) const { return x != o.x; } long long operator()() const { return x; } }; template <int m> istream &operator>>(istream &is, mod<m> &n) { long long x; is >> x; n = x; return is; } const int M = 998244353; using base = mod<M>; int main() { ios::sync_with_stdio(false); cin.tie(0); int p, s, r; cin >> p >> s >> r; int P = p + s + 5; vector<vector<base>> choose(P, vector<base>(P)); for (int i = (0); i < (P); i++) { for (int j = (0); j < (P); j++) { if (j == 0) choose[i][j] = 1; else if (i == 0) choose[i][j] = 0; else choose[i][j] = choose[i - 1][j] + choose[i - 1][j - 1]; } } base ans = 0; vector<base> f; for (int i = (1); i < (p + 1); i++) { for (int k = r; k * i <= s; k++) { base add = 0; int sum = s - i * k; int people = p - i; int mx = k - 1; if (people == 0) { if (sum == 0) add += 1; } else if (mx >= 0) { for (int j = 0; (mx + 1) * j <= sum && j <= people; j++) { base x = choose[people][j] * choose[sum - (mx + 1) * j + people - 1][people - 1]; if (j % 2 == 0) add += x; else add -= x; } } ans += choose[p - 1][i - 1] * add / i; } } base tot = choose[s - r + p - 1][p - 1]; ans /= tot; cout << ans() << '\n'; }
#include <bits/stdc++.h> using namespace std; template <class T> inline void read(T &x) { x = 0; char c = getchar(); int f = 1; while (!isdigit(c)) { if (c == '-') f = -1; c = getchar(); } while (isdigit(c)) x = x * 10 - '0' + c, c = getchar(); x *= f; } const int mod = 998244353; long long frac[6100], inv[6100]; long long Pow(long long x, long long y) { long long res = 1; while (y) { if (y & 1) res = res * x % mod; x = x * x % mod, y >>= 1; } return res; } void predo(int n) { frac[0] = 1; for (int i = 1; i <= n; ++i) frac[i] = frac[i - 1] * i % mod; inv[n] = Pow(frac[n], mod - 2); for (int i = n - 1; i >= 0; --i) inv[i] = inv[i + 1] * (i + 1) % mod; } long long C(int n, int m) { if (m > n || n < 0 || m < 0) return 0; return frac[n] * inv[m] % mod * inv[n - m] % mod; } long long solve(int s, int n, int m) { if (!n) return !s; if (n * m < s) return 0; long long ans = 0, f = -1; for (int i = 0; i <= n; ++i) f = -f, ans = (ans + f * C(n, i) * C(s - i * (m + 1) + n - 1, n - 1)) % mod; return ans; } int main() { int p, s, r; read(p), read(s), read(r); if (p == 1) return puts("1"), 0; predo(p + s); long long ans = 0; for (int j = r; j <= s; ++j) for (int k = 1; k * j <= s && k <= p; ++k) ans = (ans + solve(s - (k * j), p - k, j - 1) * C(p - 1, k - 1) % mod * Pow(k, mod - 2)) % mod; ans = ans * Pow(C(s - r + p - 1, p - 1), mod - 2) % mod; printf("%lld\n", (ans + mod) % mod); return 0; }
#include <bits/stdc++.h> using namespace std; const int hgs = 998244353, N = 5500; int fac[N], inv[N], n = 5200, s, p, r, inv2[N]; int qpow(int A, int B) { int C = 1; for (; B; B >>= 1, A = 1ll * A * A % hgs) if (B & 1) C = 1ll * A * C % hgs; return C; } void prep() { fac[0] = inv[0] = 1; for (register int i = (1); i <= (n); ++i) fac[i] = 1ll * i * fac[i - 1] % hgs; inv[n] = qpow(fac[n], hgs - 2); for (register int i = (n - 1); i >= (1); --i) inv[i] = 1ll * (i + 1) * inv[i + 1] % hgs; for (register int i = (1); i <= (n); ++i) inv2[i] = qpow(i, hgs - 2); } void upd(int &x, int y) { x = (x + y) % hgs; } void ret(int &x) { x = (x % hgs + hgs) % hgs; } int C(int A, int B) { if (A < 0 || B < 0 || B - A < 0) return 0; return 1ll * fac[B] * inv[A] % hgs * inv[B - A] % hgs; } int S(int A, int B) { return C(B - 1, A + B - 1); } int calc(int rs, int rsp, int ove) { if (rs == 0) return 1; int ans = 0; long long nw = 1; for (register int i = (0); i <= (rsp); ++i) { if (i * ove > rs) break; upd(ans, 1ll * nw * S(rs - i * ove, rsp) * C(i, rsp) % hgs); ret(ans); nw = -nw; } return ans; } int g(int x) { int rs = s - x, ans = 0; for (register int i = (0); i <= (p - 1); ++i) { if (i * x > rs) break; if ((p - 1 - i) * (x - 1) + (i + 1) * x < s) continue; upd(ans, 1ll * inv2[i + 1] * calc(rs - i * x, p - (i + 1), x) % hgs * C(i, p - 1) % hgs); } return ans; } signed main() { int ans = 0; cin >> p >> s >> r; prep(); for (register int i = (r); i <= (s); ++i) upd(ans, g(i)); int t = S(s - r, p); cout << 1ll * ans * qpow(t, hgs - 2) % hgs << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; long long n, s, r; const long long mod = 998244353; long long dp[105][5005], pw[105][5005], fact[50005], invfact[50005]; long long inv(long long a) { long long b = mod - 2; long long rez = 1; while (b) { if (b & 1) rez = (rez * a) % mod; a = (a * a) % mod; b /= 2; } return rez; } long long comb(long long a, long long b) { if (a < b) return 0; long long rez = fact[a]; rez = (rez * invfact[b]) % mod; rez = (rez * invfact[a - b]) % mod; return rez; } long long stars_and_bars(long long bile, long long urne) { return comb(bile + urne - 1, urne - 1); } int main() { cin >> n >> s >> r; for (long long i = 1; i <= n; i++) { pw[i][0] = 1; for (int j = 1; j <= s; j++) pw[i][j] = (pw[i][j - 1] * 1LL * i) % mod; } fact[0] = 1; invfact[0] = 1; for (long long i = 1; i <= 50000; i++) { fact[i] = (fact[i - 1] * i) % mod; invfact[i] = inv(fact[i]) % mod; } for (int i = 1; i <= n; i++) for (int x = 1; x <= s + 1; x++) { bool ok = 0; if (i == 2 && x == 4) ok = 1; long long lft = s - (n - i) * x; for (int nums = 0; nums <= i; nums++) { long long suma = lft - nums * x; if (suma < 0) break; long long val = (stars_and_bars(suma, i) * comb(i, nums)) % mod; if (nums % 2 == 0) { dp[i][x] = (dp[i][x] + val); if (dp[i][x] >= mod) dp[i][x] -= mod; } else { dp[i][x] = (dp[i][x] - val); if (dp[i][x] < 0) dp[i][x] += mod; } } } long long ans = 0; long long total = stars_and_bars(s - r, n); for (int nr = 1; nr < n; nr++) for (int val = r; val <= s; val++) { long long lft = n - nr; long long slft = s - val * nr; if (slft < 0) continue; long long states = (dp[lft][val] * comb(n - 1, nr - 1)) % mod; states = (states * inv(nr)) % mod; states = (states * inv(total)) % mod; ans = (ans + states) % mod; } if (s % n == 0 && s / n >= r) { long long val = (inv(n) * inv(total)) % mod; ans = (ans + val) % mod; } cout << ans; return 0; }
#include <bits/stdc++.h> using namespace std; const int MOD = 998244353; long long mod_inv(long long a, long long m = MOD) { return a == 1 ? 1 : m - mod_inv(m % a, a) * m / a; } int mod_add(int a, int b) { int sum = a + b; return sum >= MOD ? sum - MOD : sum; } int mod_sub(int a, int b) { int diff = a - b; return diff < 0 ? diff + MOD : diff; } vector<vector<long long>> choose; void prepare_choose(int max) { choose.resize(max + 1); for (int n = 0; n <= max; n++) { choose[n].resize(n + 1); choose[n][0] = choose[n][n] = 1; for (int r = 1; r < n; r++) choose[n][r] = mod_add(choose[n - 1][r - 1], choose[n - 1][r]); } } int ways_to_distribute(int score, int players) { if (score <= 0 || players <= 0) return score == 0 ? 1 : 0; return choose[score + players - 1][score]; } int ways_to_distribute_bounded(int players, int me, int sum) { int total = 0; for (int p = 0; p <= players; p++) { int ways = (long long)choose[players][p] * ways_to_distribute(sum - me * p, players) % MOD; if (p % 2 == 0) total = mod_add(total, ways); else total = mod_sub(total, ways); } return total; } int main() { int P, S, R; cin >> P >> S >> R; prepare_choose(S + P); if (P == 1) { cout << 1 << '\n'; return 0; } if (S == 0) { cout << mod_inv(P) << '\n'; return 0; } long long total = 0, denominator = 0; for (int me = R; me <= S; me++) { long long ways = ways_to_distribute(S - me, P - 1); denominator = (denominator + ways) % MOD; if (me > S - me) { total = (total + ways) % MOD; continue; } if (me * P < S) continue; int max_same = S / me; assert(max_same >= 2 && max_same <= P); for (int same = max_same; same > 0; same--) { long long less_than = ways_to_distribute_bounded(P - same, me, S - same * me); total = (total + less_than * choose[P - 1][same - 1] % MOD * mod_inv(same)) % MOD; } } total %= MOD; total = total * mod_inv(denominator) % MOD; cout << total << '\n'; }
#include <bits/stdc++.h> const int Mod = 998244353; inline int chk(int x) { if (x < 0) x += Mod; if (x >= Mod) x -= Mod; return x; } inline int qPow(int b, int e) { int a = 1; for (; e; b = (long long)b * b % Mod, e >>= 1) if (e & 1) a = (long long)a * b % Mod; return a; } int p, s, r, c[5105][105]; void Init() { for (int i = 0; i <= 5100; ++i) c[i][0] = 1; for (int i = 0; i <= 5100; ++i) for (int j = 1; j <= i && j <= 100; ++j) c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % Mod; } inline int Calc(int n, int m, int x) { long long S = 0; for (int i = 0; i <= m && i * x <= n; ++i) { long long s = (long long)c[m][i] * c[n - x * i + m - 1][m - 1] % Mod; S += i & 1 ? -s : s; } return (S % Mod + Mod) % Mod; } int Sum1, Sum2; int main() { scanf("%d%d%d", &p, &s, &r); if (p == 1) return puts("1"), 0; Init(); for (int x = r; x <= s; ++x) { if (x * p < s) continue; for (int i = 1; i <= p; ++i) { if (i * x > s || (p - i) * (x - 1) + i * x < s) continue; if (i == p) { Sum2 = (Sum2 + (i * x == s ? qPow(i, Mod - 2) : 0)) % Mod; continue; } Sum2 = (Sum2 + (long long)c[p - 1][i - 1] * Calc(s - i * x, p - i, x) % Mod * qPow(i, Mod - 2)) % Mod; } } Sum1 = c[s - r + p - 1][p - 1]; printf("%lld\n", (long long)Sum2 * qPow(Sum1, Mod - 2) % Mod); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 10006, M = 106, P = 998244353; int jc[N], jcinv[N]; inline int ksm(int a, int b) { int ans = 1; while (b) { if (b & 1) ans = (long long)ans * a % P; a = (long long)a * a % P; b >>= 1; } return ans; } inline int C(int b, int a) { if (a == b) return 1; if (a < 0 || a > b) return 0; return (long long)jc[b] * jcinv[a] % P * jcinv[b - a] % P; } inline int g(int s, int p, int x) { int ans = 0; for (int i = 0; i <= p; i++) ans = (ans + (long long)((i & 1) ? P - 1 : 1) * C(p, i) % P * C(s + p - 1 - i * (x + 1), p - 1) % P) % P; return ans; } inline int inv(int x) { return (long long)jc[x - 1] * jcinv[x] % P; } int main() { jc[0] = 1; for (int i = 1; i <= 10000; i++) jc[i] = (long long)jc[i - 1] * i % P; jcinv[10000] = ksm(jc[10000], P - 2); for (int i = 10000; i; i--) jcinv[i - 1] = (long long)jcinv[i] * i % P; int p, s, r; cin >> p >> s >> r; int ans = 0; for (int i = r; i <= s; i++) for (int j = 1; j <= p; j++) ans = (ans + (long long)C(p - 1, j - 1) * inv(j) % P * g(s - i * j, p - j, i - 1) % P) % P; cout << ((long long)ans * ksm(C(s - r + p - 1, p - 1), P - 2) % P + P) % P << endl; return 0; }
#include <bits/stdc++.h> using namespace std; int p, s, r, M = 998244353; long long iv[5100], f1[5100], f2[5100], ans; int main() { ios::sync_with_stdio(0); cin.tie(0); iv[1] = f1[0] = f1[1] = f2[0] = f2[1] = 1; for (int i = 2; i < 5100; ++i) { iv[i] = (M - M / i) * iv[M % i] % M; f1[i] = f1[i - 1] * i % M; f2[i] = f2[i - 1] * iv[i] % M; } cin >> p >> s >> r; for (int i = 1; i <= p && s - r * i >= 0; ++i) ans += (i & 1 ? 1 : -1) * f1[s - r * i + p - 1] * f2[s - r * i] % M * f2[i] % M * f2[p - i] % M; ans = (ans % M + M) * f1[p - 1] % M * f1[s - r] % M * f2[s - r + p - 1] % M; cout << ans; }
#include <bits/stdc++.h> using namespace std; long long fast(long long a, long long b) { if (a == 0) return 0; long long res = 1; while (b) { if (b & 1) res = res * a % 998244353; a = a * a % 998244353; b >>= 1; } return res; } long long frac[20005], inv[20005]; void init() { frac[1] = frac[0] = 1; for (long long i = 2; i < 20005; i++) frac[i] = frac[i - 1] * i % 998244353; inv[20005 - 1] = fast(frac[20005 - 1], 998244353 - 2); for (long long i = 20005 - 2; i >= 0; i--) inv[i] = inv[i + 1] * (i + 1) % 998244353; } long long C(long long a, long long b) { if (a == b) return 1; if (b < 0 || b > a) return 0; return frac[a] * inv[b] % 998244353 * inv[a - b] % 998244353; } long long cal(long long s, long long p, long long m) { long long res = 0; for (long long i = 0; i <= p; i++) { res += (((i & 1 ? 998244353 - 1 : 1) * (C(p, i) % 998244353 * C(s + p - 1 - i * (m + 1), p - 1) % 998244353) % 998244353) + 998244353) % 998244353; res %= 998244353; } return res; } signed main() { cin.tie(0); ios_base::sync_with_stdio(0); init(); long long p, s, r; cin >> p >> s >> r; long long ans = 0; long long tmp2 = fast(C(s - r + p - 1, p - 1), 998244353 - 2); for (long long t = r; t <= s; t++) { for (long long q = 1; q <= p; q++) { long long tmp1 = cal(s - q * t, p - q, t - 1); ans += C(p - 1, q - 1) % 998244353 * fast(q, 998244353 - 2) % 998244353 * tmp1 % 998244353; ans %= 998244353; } } cout << ans * tmp2 % 998244353 << '\n'; return 0; }
#include <bits/stdc++.h> using namespace std; long long C[5210][5010], inv[110]; long long solve(int a, int b, int lim) { if (lim < 0) return 0; if (a == 0) return 1; int i; long long tot = 0, x = 1; for (i = 0; i <= b; ++i) { if (a + b - 1 - (lim + 1) * i >= 0 && b - 1 >= 0) (tot += C[a + b - 1 - (lim + 1) * i][b - 1] * C[b][i] % 998244353ll * x) %= 998244353ll, (tot += 998244353ll) %= 998244353ll; x = -x; } return tot; } long long ksm(long long x, long long y) { long long qwq = 1; while (y) { if (y & 1) (qwq *= x) %= 998244353ll; (x *= x) %= 998244353ll, y >>= 1; } return qwq; } int main() { int s, r, p, i, j, k; long long P = 0, Q, x; scanf("%d", &p), scanf("%d", &s), scanf("%d", &r); inv[1] = 1; C[0][0] = 1; for (i = 1; i <= s + p - 1; ++i) { C[i][0] = 1; for (j = 1; j <= p; ++j) { if (j > i) C[i][j] = 0; else C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % 998244353ll; } } for (i = 2; i <= p; ++i) inv[i] = (1ll * 998244353ll - 1ll * 998244353ll / i) * inv[998244353ll % i] % 998244353ll; Q = C[s + p - 1 - r][p - 1]; for (i = max(r, s / p); i <= s; ++i) { for (j = 1; j <= p; ++j) { if (i * j > s) break; if (j == p && i * p == s) { (P += inv[p]) %= 998244353ll; continue; } (P += solve(s - i * j, p - j, i - 1) * C[p - 1][j - 1] % 998244353ll * inv[j] % 998244353ll) %= 998244353ll; } } cout << P * ksm(Q, 998244353ll - 2) % 998244353ll; }
#include <bits/stdc++.h> using namespace std; template <class T> inline void chkmin(T &a, T b) { if (a > b) a = b; } template <class T> inline void chkmax(T &a, T b) { if (a < b) a = b; } inline int read() { int s = 0, f = 1; char ch = getchar(); while (!isdigit(ch) && ch != '-') ch = getchar(); if (ch == '-') ch = getchar(), f = -1; while (isdigit(ch)) s = s * 10 + ch - '0', ch = getchar(); return ~f ? s : -s; } const int mod = 998244353; int inv[50020], jc[50020], jcn[50020]; inline int power(int a, int b) { int ans = 1; while (b) { if (b & 1) ans = (long long)ans * a % mod; b >>= 1; a = (long long)a * a % mod; } return ans; } inline int C(int n, int m) { if (n < 0 || n < m) return 0; return 1ll * jc[n] * jcn[m] % mod * jcn[n - m] % mod; } int n, m, r; inline void init() { jc[0] = jc[1] = jcn[0] = jcn[1] = inv[1] = 1; for (int i = (2), _end_ = (5e4); i <= _end_; i++) inv[i] = (long long)(mod - mod / i) * inv[mod % i] % mod, jc[i] = (long long)jc[i - 1] * i % mod, jcn[i] = (long long)jcn[i - 1] * inv[i] % mod; n = read(); m = read(); r = read(); } inline void doing() { int ans = 0, fas = 0; fas = C(m - r + n - 1, n - 1); for (int x = (r), _end_ = (m); x <= _end_; x++) { for (int num = (1), _end_ = (n); num <= _end_; num++) if (num * x <= m) { int rest = m - num * x, renum = n - num, xs = (long long)inv[num] * C(n - 1, num - 1) % mod; if (renum == 0) { if (rest == 0) ans = (ans + xs) % mod; } else { for (int j = (0), _end_ = (n - num); j <= _end_; j++) { int re = rest - j * x; if (re >= 0) ans = (ans + (j & 1 ? -1 : 1) * (long long)C(re + renum - 1, renum - 1) * xs % mod * C(renum, j)) % mod; } } } } ans = (ans + mod) % mod; ans = (long long)ans * power(fas, mod - 2) % mod; printf("%d\n", ans); } int main() { init(); doing(); return 0; }
#include <bits/stdc++.h> using namespace std; long long read() { long long nm = 0, fh = 1; char cw = getchar(); for (; !isdigit(cw); cw = getchar()) if (cw == '-') fh = -fh; for (; isdigit(cw); cw = getchar()) nm = nm * 10 + (cw - '0'); return nm * fh; } long long n, m, fac[100020], ifac[100020], S, R, sum, ans; long long qpow(long long x, long long sq) { long long res = 1; for (; sq; sq >>= 1, x = x * x % 998244353) if (sq & 1) res = res * x % 998244353; return res; } long long C(long long tot, long long tk) { if (tot < 0 || tk < 0 || tot < tk) return 0ll; return fac[tot] * ifac[tk] % 998244353 * ifac[tot - tk] % 998244353; } long long dev(long long tot, long long tk) { if (!tk) { return (tot != 0 ? 0 : 1); } if (tot < 0) return 0; return C(tot + tk - 1, tk - 1); } int main() { n = read(), m = read(), R = read(), fac[0] = 1; for (long long i = 1; i < 100020; i++) fac[i] = fac[i - 1] * i % 998244353; ifac[100020 - 1] = qpow(fac[100020 - 1], 998244353 - 2); for (long long i = 100020 - 1; i; i--) ifac[i - 1] = ifac[i] * i % 998244353; for (long long gg = R; gg <= m; gg++) { long long res = 0, rem = m - gg; for (long long ev = 0; ev < n; ev++) { long long now = 0, rst = rem - ev * gg; if (rst < 0) break; for (long long i = 0, kd = 1; i <= n - ev - 1; i++, kd = -kd) now += kd * C(n - 1 - ev, i) * dev(rst - i * gg, n - 1 - ev) % 998244353, now %= 998244353; ans += qpow(ev + 1, 998244353 - 2) * C(n - 1, ev) % 998244353 * (now + 998244353) % 998244353, (ans >= 998244353) ? (ans -= 998244353) : 0; } } printf("%lld\n", ans * qpow(dev(m - R, n), 998244353 - 2) % 998244353); return 0; }
#include <bits/stdc++.h> using namespace std; const int maxn = 1e5 + 233; int fac[maxn], inv[maxn]; const int mod = 998244353; int p, s, r; void add(int &x, int y) { x += y; if (x >= mod) x -= mod; } void sub(int &x, int y) { x -= y; if (x < 0) x += mod; } int pow_mod(int q, int w) { int ret = 1; while (w) { if (w & 1) ret = 1ll * ret * q % mod; q = 1ll * q * q % mod; w >>= 1; } return ret; } int rev(int x) { return 1ll * inv[x] * fac[x - 1] % mod; } int C(int x, int y) { if (x < 0 || y < 0) return 0; if (x < y) return 0; return 1ll * fac[x] * inv[y] % mod * inv[x - y] % mod; } int main() { ios::sync_with_stdio(false), cin.tie(0), cout.tie(0); fac[0] = inv[0] = 1; for (int i = 1; i < maxn; i++) { fac[i] = 1ll * fac[i - 1] * i % mod; inv[i] = pow_mod(fac[i], mod - 2); } cin >> p >> s >> r; if (s == 0) { cout << pow_mod(p, mod - 2) << "\n"; return 0; } int all = 0; int res = 0; for (int mx = r; mx <= s; mx++) { if (p == 1) { if (mx == s) add(all, 1); } else add(all, C(s - mx + p - 2, p - 2)); if (mx == 0) { continue; } for (int cnt = 1; cnt <= min(p, s / mx); cnt++) { int left = s - cnt * mx; int y = p - cnt; if (y == 0) { if (left == 0) { add(res, rev(cnt)); } continue; } int tmp = 0; for (int t = left % mx; t <= left; t += mx) { assert((left - t) % mx == 0); int times = 1ll * C(y + t - 1, t) * C(y, (left - t) / mx) % mod * C(p - 1, cnt - 1) % mod; if (((left - t) / mx) % 2) sub(tmp, times); else add(tmp, times); } add(res, 1ll * tmp * rev(cnt) % mod); } } cout << 1ll * res * pow_mod(all, mod - 2) % mod << "\n"; return 0; }
#include <bits/stdc++.h> using namespace std; const int mod = 998244353; const int N = 5001; int ans; int ni[101]; int a[N * 2], nia[N * 2], f[N + 10]; int n, r, s; long long calc(long long x, long long y) { long long z = 1; while (y) { if (y & 1) z = z * x % mod; x = x * x % mod, y /= 2; } return z; } long long CC(int x, int y) { return y < 0 || x < y ? 0 : 1ll * a[x] * nia[y] % mod * nia[x - y] % mod; } int add(int x, int y) { x += y; return x >= mod ? x - mod : x; } int sub(int x, int y) { x -= y; return x < 0 ? x + mod : x; } int mul(int x, int y) { return 1ll * x * y % mod; } int get(int n, int s, int k) { if (s < 0 || s > k * n) return 0; if (!n && !s) return 1; int v = 0; int nn = (k >= 0 ? max(min(n, s / (k + 1)), 0) + 1 : 0); for (int i = 0; i <= nn; i++) f[i] = 0; for (int i = nn; i >= 0; i--) { f[i] = mul(CC(n, i), CC(s - (k + 1) * i + n - 1, n - 1)); for (int j = i + 1; j <= nn; j++) f[i] = sub(f[i], mul(f[j], CC(j, i))); } v = f[0]; return v; } int main() { scanf("%d %d %d", &n, &s, &r); a[0] = 1; for (int i = 1; i < N * 2; i++) a[i] = 1ll * a[i - 1] * i % mod; nia[N * 2 - 1] = calc(a[N * 2 - 1], mod - 2); for (int i = N * 2 - 2; i >= 0; i--) nia[i] = 1ll * nia[i + 1] * (i + 1) % mod; ni[0] = ni[1] = 1; for (int i = 2; i <= n; i++) ni[i] = 1ll * ni[mod % i] * (mod - mod / i) % mod; for (int i = n; i >= 1; i--) { for (int j = r; j * i <= s; j++) ans = (ans + 1ll * CC(n - 1, i - 1) * get(n - i, s - j * i, min(j - 1, s - j * i)) % mod * ni[i]) % mod; } long long all = 0; if (n == 1 && r <= s) all = 1; for (int j = r; j <= s; j++) all = add(all, CC(s - j + n - 2, n - 2)); printf("%lld\n", ans * calc(all, mod - 2) % mod); return 0; }
#include <bits/stdc++.h> using namespace std; inline void read(long long &x) { char ch; bool flag = false; for (ch = getchar(); !isdigit(ch); ch = getchar()) if (ch == '-') flag = true; for (x = 0; isdigit(ch); x = x * 10 + ch - '0', ch = getchar()) ; x = flag ? -x : x; } inline void write(long long x) { static const long long maxlen = 100; static char s[maxlen]; if (x < 0) { putchar('-'); x = -x; } if (!x) { putchar('0'); return; } long long len = 0; for (; x; x /= 10) s[len++] = x % 10 + '0'; for (long long i = len - 1; i >= 0; --i) putchar(s[i]); } inline void read(int &x) { char ch; bool flag = false; for (ch = getchar(); !isdigit(ch); ch = getchar()) if (ch == '-') flag = true; for (x = 0; isdigit(ch); x = x * 10 + ch - '0', ch = getchar()) ; x = flag ? -x : x; } template <typename T> T gcd(T m, T n) { if (!m || !n) return m | n; if (m < 0) m = -m; if (n < 0) n = -n; long long p = 0; while (!(m & 1) && !(n & 1)) m >>= 1, n >>= 1, ++p; while (n) { while (!(m & 1)) m >>= 1; while (!(n & 1)) n >>= 1; if (m >= n) std::swap(m, n); n = (n - m) >> 1; } return m << p; } template <typename T> std::pair<T, std::pair<T, T> > exgcd(T m, T n) { using std::make_pair; T x = 0, y = 1, xp = 1, yp = 0, xt, yt; for (T r = m % n, q = m / n; r;) { xt = xp - q * x, xp = x, x = xt; yt = yp - q * y, yp = y, y = yt; m = n, n = r, r = m % n, q = m / n; } return make_pair(n, make_pair(x, y)); } template <typename T> T modinv(T m, T n) { std::pair<T, std::pair<T, T> > gxy = exgcd(m, n); T loop = n / gxy.first; T inv = gxy.second.first; inv = inv % loop; return inv < 0 ? inv + loop : inv; } const long long MAX_S = 5500; long long C[MAX_S][MAX_S]; const long long P = 998244353; long long get_C(long long n, long long m) { if (n < m) return 0; if (n < 0) return 0; if (m < 0) return 0; return C[n][m]; } void prepare() { C[0][0] = 1; for (long long i = 1; i < MAX_S; i++) { for (long long j = 0; j <= i; j++) C[i][j] = (C[i - 1][j - 1] + C[i - 1][j]) % P; } } long long get_ans(long long n, long long s, long long lim) { if (n == 0) return (s == 0) ? 1 : 0; if (lim < 0) return 0; if (n < 0) return 0; if (s < 0) return 0; long long ans = get_C(s + n - 1, n - 1); long long op = -1; for (long long m = 1; m <= n; m++) { ans = ((ans + op * get_C(s - (lim + 1) * m + n - 1, n - 1) * get_C(n, m) % P) % P + P) % P; op = -op; } return ans; } long long n, s, r; int main() { prepare(); read(n); read(s); read(r); long long ans = 0; for (long long i = r; i <= s; i++) for (long long j = 1; (i * j <= s) && (j <= n); j++) { ans = ((ans + 1ll * get_ans(n - j, s - i * j, i - 1) * get_C(n - 1, j - 1) % P * modinv(j, P) % P) % P + P) % P; } ans = 1ll * ans * modinv(get_C((s - r) + n - 1, n - 1), P) % P; cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const long long M = 10006; long long f[M], inv[M]; long long expo(long long base, long long exponent, long long mod) { long long ans = 1; while (exponent != 0) { if (exponent & 1) ans = (1LL * ans * base) % mod; base = (1LL * base * base) % mod; exponent >>= 1; } return ans % mod; } void compute() { f[0] = 1; for (long long i = 1; i < M; i++) { f[i] = (1LL * i * f[i - 1]) % 998244353; } inv[M - 1] = expo(f[M - 1], 998244353 - 2, 998244353); for (long long i = M - 2; i >= 0; i--) { inv[i] = (1LL * (i + 1) * inv[i + 1]) % 998244353; } } long long C(long long n, long long r) { return (1LL * ((1LL * f[n] * inv[r]) % 998244353) * inv[n - r]) % 998244353; } long long ff(long long n, long long s, long long u) { if (n == 0) return s == 0; if (s < 0 or u < 0) return 0; long long ans = 0; for (long long r = 0; r < n + 1; r++) { long long k = s - (u + 1) * r; if (k < 0) break; if (r % 2) { ans = (ans - C(n, r) * C(n + k - 1, k) % 998244353 + 998244353) % 998244353; } else { ans = (ans + C(n, r) * C(n + k - 1, k) % 998244353 + 998244353) % 998244353; } } return ans; } long long inverse[1001]; void solve() { compute(); for (long long i = 1; i < 1001; i++) inverse[i] = expo(i, 998244353 - 2, 998244353); long long p, s, r, ans = 0, den = 0; cin >> p >> s >> r; for (long long i = r; i < s + 1; i++) { for (long long j = 1; j < p + 1; j++) { ans = (ans + C(p - 1, j - 1) * ff(p - j, s - j * i, i - 1) % 998244353 * inverse[j] % 998244353) % 998244353; } den = (den + ff(p - 1, s - i, s)) % 998244353; } ans = ans * expo(den, 998244353 - 2, 998244353) % 998244353; cout << ans << '\n'; } signed main() { ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); long long t = 1; while (t--) { solve(); } return 0; }
#include <bits/stdc++.h> const int N = 6010; const int moder = 998244353; int comb[N][N]; void init() { for (int i = 0; i < N; ++i) { comb[i][0] = 1; for (int j = 1; j <= i; ++j) { comb[i][j] = (comb[i - 1][j - 1] + comb[i - 1][j]) % moder; } } } int sol(int n, int sum) { return comb[n + sum - 1][n - 1]; } int powermod(int a, int exp) { int ret = 1; for (; exp > 0; exp >>= 1) { if (exp & 1) { ret = 1ll * ret * a % moder; } a = 1ll * a * a % moder; } return ret; } int main() { init(); int p, s, r; scanf("%d%d%d", &p, &s, &r); int ans = 0; for (int i = r; i <= s; ++i) { for (int j = 0; j < p && (j + 1) * i <= s; ++j) { int sum = 0, cnt = p - j - 1, left = s - (j + 1) * i; if (!cnt) { if (!left) { sum = 1; } } else { for (int k = 0; k <= cnt && k * i <= left; ++k) { sum = (sum + (k & 1 ? -1ll : 1ll) * comb[cnt][k] * sol(cnt, left - k * i)) % moder; } } ans = (ans + 1ll * sum * comb[p - 1][j] % moder * powermod(j + 1, moder - 2)) % moder; } } ans += ans < 0 ? moder : 0; ans = 1ll * ans * powermod(sol(p, s - r), moder - 2) % moder; printf("%d\n", ans); }
#include <bits/stdc++.h> using namespace std; const long long mod = 998244353; long long C[5110][110], ans; void pre() { for (int i = 0; i <= 5100; i++) { C[i][0] = 1; for (int j = 1; j <= i && j <= 100; j++) { C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod; } } } long long qpow(long long a, long long x) { long long res = 1; while (x) { if (x & 1) { res = res * a % mod; } a = a * a % mod; x >>= 1; } return res; } long long Comb(int n, int m) { if (n < m) return 0; return C[n][m]; } long long calc(int s, int n, int r) { long long res = 0; for (int i = 0; i <= n; i++) { long long tmp = C[n][i] * Comb(s - i * r + n - 1, n - 1) % mod; if (i & 1) { res -= tmp; if (res < 0) res += mod; } else { res += tmp; if (res >= mod) res -= mod; } } return res; } int n, s, r; int main() { scanf("%d %d %d", &n, &s, &r); pre(); if (n == 1) { printf("1\n"); return 0; } for (int i = r; i <= s; i++) { for (int j = 0; j < n; j++) { if (j == n - 1) { ans += i * n == s ? qpow(j + 1, mod - 2) : 0; if (ans >= mod) ans -= mod; continue; } ans += (C[n - 1][j] * calc(s - i * (j + 1), n - j - 1, i) % mod) * qpow(j + 1, mod - 2) % mod; if (ans >= mod) ans -= mod; } } printf("%lld\n", ans * qpow(Comb(s - r + n - 1, n - 1), mod - 2) % mod); return 0; }
#include <bits/stdc++.h> using namespace std; const long long mod = 998244353; int p, s, r; long long fac[10005]; long long qpow(long long x, int y) { long long sum = 1; while (y) { if (y & 1) { sum = sum * x % mod; } x = x * x % mod; y >>= 1; } return sum; } long long ny(int x) { return qpow(x, mod - 2); } long long C(int n, int m) { if (n < m || n < 0 || m < 0) return 0; return fac[n] * ny(fac[m]) % mod * ny(fac[n - m]) % mod; } long long f(int n, int m, int lim) { if (n == 0) return 1; if (n < 0) return 0; long long sum = 0; for (int i = 0; i <= m; i++) { long long t = (i & 1) ? (mod - 1ll) : 1ll; sum = (sum + t * C(m, i) % mod * C(n - i * lim + m - 1ll, m - 1ll) % mod) % mod; } return sum; } int main() { scanf("%d%d%d", &p, &s, &r); fac[0] = 1; for (int i = 1; i <= 6000; i++) { fac[i] = fac[i - 1] * i % mod; } long long ans = 0; for (int i = r; i <= s; i++) { for (int j = 1; j <= p; j++) { if ((p - j) * (i - 1) + j * i < s) continue; ans = (ans + f(s - i * j, p - j, i) * C(p - 1, j - 1) % mod * ny(j) % mod) % mod; } } printf("%lld", ans * ny(C(s - r + p - 1, p - 1)) % mod); return 0; }
#include <bits/stdc++.h> using namespace std; const long long MOD = 998244353; const int MAXN = 5555; long long fac[MAXN], ifac[MAXN]; long long binom(long long n, long long k) { if (k > n || k < 0) return 0; long long ans = (ifac[k] * ifac[n - k]) % MOD; return (ans * fac[n]) % MOD; } long long inv(long long b) { long long e = MOD - 2, res = 1; for (long long k = 1; k <= e; k *= 2) { if (k & e) res = (res * b) % MOD; b = (b * b) % MOD; } return res; } long long awoo(long long p, long long ts, long long bn) { if (p == 0) { if (ts == 0) return 1; else return 0; } long long res = 0; for (long long meanies = 0; meanies * bn <= ts; meanies++) { if (meanies > p) break; long long cnt = (binom(p, meanies) * binom(ts - meanies * bn + p - 1, p - 1)) % MOD; if (meanies % 2) res = (res - cnt) % MOD; else res = (res + cnt) % MOD; } return (res + MOD) % MOD; } int main() { fac[0] = 1; for (int i = 1; i < MAXN; i++) fac[i] = (i * fac[i - 1]) % MOD; ifac[MAXN - 1] = inv(fac[MAXN - 1]); for (int i = MAXN - 1; i >= 1; i--) ifac[i - 1] = (i * ifac[i]) % MOD; long long p, s, r, ans = 0, ways = 0; cin >> p >> s >> r; if (p == 1) { cout << "1\n"; return 0; } if (r == 0) { cout << inv(p) << '\n'; return 0; } for (long long sc = r; sc <= s; sc++) { ways = (ways + binom(s - sc + p - 2, p - 2)) % MOD; for (long long np = 1; np * sc <= s; np++) { if (np > p) break; long long res = (awoo(p - np, s - np * sc, sc) * inv(np)) % MOD; res = (res * binom(p - 1, np - 1)) % MOD; ans += res; if (ans >= MOD) ans -= MOD; } } cout << (ans * inv(ways)) % MOD << '\n'; }
#include <bits/stdc++.h> using namespace std; const long long mod = 998244353; long long pw(long long x, long long y) { if (y == 0) return 1; if (y % 2) return x * pw(x, y - 1) % mod; long long res = pw(x, y / 2); return res * res % mod; } long long f[10001]; long long inf[10001]; long long inv[10001]; long long C(int x, int y) { return f[x] * inf[y] % mod * inf[x - y] % mod; } int p, r, s; long long dp[101]; int main() { ios::sync_with_stdio(false); f[0] = inf[0] = 1; for (int i = 1; i <= 10000; i++) { f[i] = f[i - 1] * i % mod; inf[i] = pw(f[i], mod - 2); inv[i] = pw(i, mod - 2); } cin >> p >> s >> r; if (p == 1) { cout << 1 << endl; return 0; } long long ans = 0; p--; long long ways = 0; for (int i = r; i <= s; i++) { if (i == 0) { if (s == 0) ans = (ans + inv[p + 1]) % mod; ways = (ways + C(s - i + p - 1, p - 1)) % mod; continue; } for (int j = 0; j <= p; j++) { int cs = s - i * (j + 1); int cp = p - j; if (cs < 0) continue; for (int k = min(cp, cs / i); k >= 0; k--) { int ccs = cs - k * i; if (cp > 0) dp[k] = C(ccs + cp - 1, cp - 1) * C(cp, k) % mod; else dp[k] = (cs == 0); for (int l = min(cp, cs / i); l > k; l--) { dp[k] = (dp[k] + (mod - C(l, k)) * dp[l]) % mod; } } ans = (ans + dp[0] * C(p, j) % mod * inv[j + 1]) % mod; } ways = (ways + C(s - i + p - 1, p - 1)) % mod; } cout << ans * pw(ways, mod - 2) % mod << endl; }
#include <bits/stdc++.h> #pragma GCC optimize("O2") using namespace std; const int N = 1e6 + 10; const long long mod2 = 1e9 + 7; const long long mod = 998244353; const long long inf = 8e18; const int LOG = 22; long long pw(long long a, long long b, long long M) { return (!b ? 1 : (b & 1 ? (a * pw(a * a % M, b / 2, M)) % M : pw(a * a % M, b / 2, M))); } long long first[N], I[N]; inline long long E(long long r, long long n) { if (r > n || r < 0) return 0ll; return first[n] * I[r] % mod * I[n - r] % mod; } long long calc(int n, int m, int s) { if (n == 0 && m == 0) return 1; long long ret = 0; for (int i = 0; i <= n; i++) { if (m < s * i) continue; long long z = (i % 2 == 0 ? 1 : -1); long long cu = E(i, n) * E(n - 1, m - s * i + n - 1) % mod; ret = (ret + z * cu + 2 * mod) % mod; } return ret; } int main() { int n, second, R; first[0] = 1; for (int i = 1; i < N; i++) { first[i] = first[i - 1] * i % mod; } I[N - 1] = pw(first[N - 1], mod - 2, mod); for (int i = N - 2; ~i; i--) I[i] = I[i + 1] * (i + 1) % mod; scanf("%d%d%d", &n, &second, &R); if (n == 1) { return !printf("1"); } long long kol = 0, win = 0; for (int T = R; T <= second; T++) { for (int i = 0; i < n; i++) { if ((i + 1) * T > second) continue; long long cu = E(i, n - 1); cu = cu * calc(n - i - 1, second - (i + 1) * T, T) % mod; win = (win + cu * pw(i + 1, mod - 2, mod)) % mod; } kol = (kol + E(n - 2, second - T + n - 2)) % mod; } long long tot = win * pw(kol, mod - 2, mod) % mod; printf("%lld ", tot); return 0; }
#include <bits/stdc++.h> using namespace std; const int mod = 998244353; const int N = 1e5 + 5; long long fac[N], inv[N]; long long bp(long long a, long long p) { long long r = 1; while (p > 0) { if (p & 1) r = r * a % mod; p >>= 1; a = a * a % mod; } return r; } long long c(int n, int k) { return fac[n] * inv[k] % mod * inv[n - k] % mod; } long long f(int s, int p, int u) { if (p == 0) { if (s == 0) return 1; return 0; } long long a = 0; for (int j = 0; j <= min(p, s / u); j++) { a = (a + c(p, j) * c(s - j * u + p - 1, p - 1) % mod * ((j & 1) ? -1 : 1) + mod) % mod; } return a; } signed main() { ios_base::sync_with_stdio(0); cin.tie(0); fac[0] = inv[0] = 1; for (int i = 1; i < N; i++) { fac[i] = fac[i - 1] * i % mod; inv[i] = bp(fac[i], mod - 2); } int p, s, r; cin >> p >> s >> r; if (r == 0 && s == 0) { cout << bp(p, mod - 2); return 0; } long long Q = c(s - r + p - 1, p - 1), P = 0; for (int i = max(r, 1); i <= s; i++) { for (int j = 1; j <= s / i; j++) { P = (P + c(p - 1, j - 1) * f(s - j * i, p - j, i) % mod * bp(j, mod - 2)) % mod; } } cout << P * bp(Q, mod - 2) % mod; return 0; }
#include <bits/stdc++.h> using namespace std; void fastIO() { std::ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); } template <typename T, typename U> inline void mnze(T &x, U y) { if (y < x) x = y; } template <typename T, typename U> inline void mxze(T &x, U y) { if (x < y) x = y; } void _scan(int &x) { scanf("%d", &x); } void _scan(long long &x) { scanf("%lld", &x); } void _scan(double &x) { scanf("%lf", &x); } void _scan(char &x) { scanf(" %c", &x); } void _scan(char *x) { scanf("%s", x); } void scan() {} template <typename T, typename... U> void scan(T &head, U &...tail) { _scan(head); scan(tail...); } template <typename T> void _dbg(const char *sdbg, T h) { cerr << sdbg << "=" << h << "\n"; } template <typename T, typename... U> void _dbg(const char *sdbg, T h, U... t) { while (*sdbg != ',') cerr << *sdbg++; cerr << "=" << h << ","; _dbg(sdbg + 1, t...); } const long long MOD = 998244353; const int MAXN = 2e5; long long sq(long long x) { return x * x % MOD; } long long pot(long long b, long long e) { return e ? sq(pot(b, e >> 1)) * (e & 1 ? b : 1) % MOD : 1; } long long inv(long long x) { return pot(x, MOD - 2); } long long fact[MAXN], ifact[MAXN]; long long comb(int n, int k) { if (k > n) return 0; return fact[n] * ifact[n - k] % MOD * ifact[k] % MOD; } long long d(int k, int n) { return comb(n + k - 1, k - 1); } void pre() { fact[0] = 1; for (int i = 1; i < (int)MAXN; i++) fact[i] = (fact[i - 1] * i) % MOD; for (int i = 0; i < (int)MAXN; i++) ifact[i] = inv(fact[i]); } long long p, r, s; int main() { pre(); scan(p, s, r); long long totalw = d(p, s - r); long long P = 0; for (int x = r; x < (int)s + 1; x++) { for (int k = 0; k < (int)p; k++) { long long n = p - 1 - k, y = s - (k + 1) * x; long long PP = comb(p - 1, k) * inv(k + 1) % MOD; if (n == 0) { if (y == 0) { P += PP; P %= MOD; } } else { long long ret = 0, sig = 1; for (int i = 0; i < (int)n + 1; i++) { long long r = (sig * comb(n, i) + MOD) % MOD; r = r * d(n, y - i * x) % MOD; ret = (ret + r) % MOD; sig *= -1; } assert(y >= 0 || ret == 0); P += ret * PP % MOD; P %= MOD; } } } long long PQ = P * inv(totalw); printf("%lld\n", (PQ % MOD + MOD) % MOD); }
#include <bits/stdc++.h> using namespace std; const int MOD = 998244353; int powerMod(int a, int n, int m) { if (!n) return 1; int t = powerMod(a, n >> 1, m); t = (1LL * t * t) % m; if (n & 1) t = (1LL * t * a) % m; return t; } const int maxN = 1e4 + 5; int fac[maxN], inv[maxN]; void computeFactorials(int n) { fac[0] = 1; for (int i = 1; i <= n; i++) fac[i] = (1LL * i * fac[i - 1]) % MOD; inv[n] = powerMod(fac[n], MOD - 2, MOD); for (int i = n - 1; i >= 0; i--) inv[i] = (1LL * inv[i + 1] * (i + 1)) % MOD; } int combi(int n, int k) { if (n == k) return 1; int res = (1LL * inv[k] * inv[n - k]) % MOD; res = (1LL * res * fac[n]) % MOD; return res; } int star(int n, int k) { return combi(n + k - 1, k - 1); } int countGame(int n, int k, int x) { int ans = 0, sign = +1; bool debug = k == 0; int remain = n; for (int i = 0; i <= k and remain >= 0; i++) { int cnt = (1LL * combi(k, i) * star(remain, k)) % MOD; (ans += sign * cnt) %= MOD; (ans += MOD) %= MOD; remain -= x; sign *= -1; } return ans; } int main() { ios::sync_with_stdio(false); cin.tie(nullptr); computeFactorials(maxN - 3); int p, s, r; cin >> p >> s >> r; int gameSize = star(s - r, p); int answer = 0; for (int x = r; x <= s; x++) { int sum = x; for (int i = 0; sum <= s and i + 1 <= p; i++) { int pick = combi(p - 1, i); int prob = (1LL * pick * countGame(s - sum, p - 1 - i, x)) % MOD; prob = (1LL * prob * powerMod(gameSize, MOD - 2, MOD)) % MOD; prob = (1LL * prob * powerMod(i + 1, MOD - 2, MOD)) % MOD; (answer += prob) %= MOD; sum += x; } } cout << answer; }
#include <bits/stdc++.h> using namespace std; const long long MOD = 998244353; const int N = 10000 + 10; int p, s, r; long long fac[N], inv[N], rev[N]; long long mpow(long long a, long long x) { if (x == 0) return 1; long long t = mpow(a, x >> 1); if (x % 2 == 0) return t * t % MOD; return t * t % MOD * a % MOD; } long long c(int a, int b) { if (a < b) return 0; if (a == b) return 1; return fac[a] * inv[b] % MOD * inv[a - b] % MOD; } long long cac(int n, int m, int k) { long long ret = 0; for (int i = 0; i <= n; i++) { if (m >= (k + 1) * i) { long long tmp = c(n, i) * c(m - (k + 1) * i + n - 1, n - 1) % MOD; if (i % 2 == 1) ret = (ret - tmp + MOD) % MOD; else ret = (ret + tmp) % MOD; } } return ret; } int main() { fac[0] = 1; inv[0] = 1; rev[0] = 1; for (int i = 1; i < N; i++) { rev[i] = mpow(i, MOD - 2); fac[i] = fac[i - 1] * i % MOD; inv[i] = mpow(fac[i], MOD - 2); } cin >> p >> s >> r; long long tot = 0; for (int i = r; i <= s; i++) { tot = (tot + c(s - i + (p - 2), (p - 2))) % MOD; } tot = mpow(tot, MOD - 2); long long res = 0; for (int i = r; i <= s; i++) { for (int j = 0; j <= p - 1; j++) { if (s - i - j * i >= 0) { res = res + rev[j + 1] * c(p - 1, j) % MOD * cac(p - 1 - j, s - i - j * i, i - 1) % MOD * tot % MOD; res %= MOD; } } } cout << res << endl; }
#include <bits/stdc++.h> using namespace std; const int maxn = 5210; const long long mod = 998244353; long long C[maxn][maxn]; long long f(int n, int m, int x) { long long ans = 0; if (!m) return (n == 0 && x > 0); for (int i = 0, s = 1; i <= m; i++, s *= -1) { if (n - i * x < 0) break; ans += s * (C[m][i] * C[n - i * x + m - 1][m - 1] % mod), (ans += mod) %= mod; } return ans; } long long poww(long long a, int b) { long long res = 1; while (b) { if (b & 1) res *= a, res %= mod; a *= a, a %= mod; b >>= 1; } return res; } int main() { for (int i = 0; i <= 5200; i++) for (int j = 0; j <= i; j++) C[i][j] = (j == 0 || j == i) ? 1 : (C[i - 1][j - 1] + C[i - 1][j]) % mod; int r, p, s; cin >> p >> s >> r; long long ans = 0; if (p == 1) { puts("1"); return 0; } if (s == 0 && r == 0) { printf("%lld\n", poww(p, mod - 2)); return 0; } for (int x = r; x <= s; x++) { for (int i = 1; i <= p; i++) { if (i * x > s) break; ans += C[p - 1][i - 1] * f(s - i * x, p - i, x) % mod * poww(i, mod - 2) % mod; ans %= mod; } } cout << ans * poww(C[s - r + p - 1][p - 1], mod - 2) % mod << endl; return 0; }
#include <bits/stdc++.h> const int Mod = 998244353; inline int chk(int x) { if (x < 0) x += Mod; if (x >= Mod) x -= Mod; return x; } inline int qPow(int b, int e) { int a = 1; for (; e; b = (long long)b * b % Mod, e >>= 1) if (e & 1) a = (long long)a * b % Mod; return a; } int p, s, r, c[5105][105]; void Init() { for (int i = 0; i <= 5100; ++i) c[i][0] = 1; for (int i = 0; i <= 5100; ++i) for (int j = 1; j <= i && j <= 100; ++j) c[i][j] = (c[i - 1][j - 1] + c[i - 1][j]) % Mod; } inline int Calc(int n, int m, int x) { long long S = 0; for (int i = 0; i <= m && i * x <= n; ++i) { long long s = (long long)c[m][i] * c[n - x * i + m - 1][m - 1] % Mod; S += i & 1 ? -s : s; } return (S % Mod + Mod) % Mod; } int Sum1, Sum2; int main() { scanf("%d%d%d", &p, &s, &r); if (p == 1) return puts("1"), 0; Init(); for (int x = r; x <= s; ++x) { if (x * p < s) continue; for (int i = 1; i <= p; ++i) { if (i * x > s || (p - i) * (x - 1) + i * x < s) continue; if (i == p) { Sum2 = (Sum2 + (i * x == s ? qPow(i, Mod - 2) : 0)) % Mod; continue; } Sum2 = (Sum2 + (long long)c[p - 1][i - 1] * Calc(s - i * x, p - i, x) % Mod * qPow(i, Mod - 2)) % Mod; } } Sum1 = c[s - r + p - 1][p - 1]; printf("%lld\n", (long long)Sum2 * qPow(Sum1, Mod - 2) % Mod); return 0; }
#include <bits/stdc++.h> using namespace std; using lint = long long; template <class T = int> using V = vector<T>; template <class T = int> using VV = V<V<T> >; template <unsigned P> struct ModInt { using M = ModInt; unsigned v; ModInt() : v(0) {} template <class Int> ModInt(Int x) : v(x >= 0 ? x % P : -x % P ? P - -x % P : 0) {} constexpr ModInt(unsigned v, int) : v(v) {} static constexpr unsigned p() { return P; } M operator+() const { return *this; } M operator-() const { return {v ? P - v : 0, 0}; } explicit operator bool() const noexcept { return v; } bool operator!() const noexcept { return !(bool)*this; } M operator*(M rhs) const { return M(*this) *= rhs; } M operator/(M rhs) const { return M(*this) /= rhs; } M operator+(M rhs) const { return M(*this) += rhs; } M operator-(M rhs) const { return M(*this) -= rhs; } bool operator==(M rhs) const { return v == rhs.v; } bool operator!=(M rhs) const { return !(*this == rhs); } M& operator*=(M rhs) { v = (unsigned long long)v * rhs.v % P; return *this; } M& operator/=(M rhs) { return *this *= rhs.inv(); } M& operator+=(M rhs) { v = rhs.v < P - v ? v + rhs.v : v - (P - rhs.v); return *this; } M& operator-=(M rhs) { v = rhs.v <= v ? v - rhs.v : v + (P - rhs.v); return *this; } M inv() const { int a = v, b = P, x = 1, u = 0; while (b) { int q = a / b; swap(a -= q * b, b); swap(x -= q * u, u); } assert(a == 1); return x; } template <class Int> M pow(Int n) const { n = n >= 0 ? n % (P - 1) : P - 1 - -n % (P - 1); M res = 1; for (M a = *this; n; a *= a, n >>= 1) if (n & 1) res *= a; return res; } template <class Int> friend M operator*(Int lhs, M rhs) { return M(lhs) *= rhs; } template <class Int> friend M operator/(Int lhs, M rhs) { return M(lhs) /= rhs; } template <class Int> friend M operator+(Int lhs, M rhs) { return M(lhs) += rhs; } template <class Int> friend M operator-(Int lhs, M rhs) { return M(lhs) -= rhs; } friend ostream& operator<<(ostream& os, M rhs) { return os << rhs.v; } friend istream& operator>>(istream& is, M& rhs) { lint x; is >> x; rhs = x; return is; } template <class Int> friend bool operator==(Int lhs, M rhs) { return M(lhs) == rhs; } template <class Int> friend bool operator!=(Int lhs, M rhs) { return !(lhs == rhs); } }; using Mint = ModInt<998244353>; V<Mint> fact, ifact; void init(int n) { fact.resize(n + 1); fact[0] = 1; for (int i = 1; i <= n; ++i) { fact[i] = i * fact[i - 1]; } ifact.resize(n + 1); ifact[n] = fact[n].inv(); for (int i = n; i > 0; --i) { ifact[i - 1] = i * ifact[i]; } } Mint comb(int n, int r) { if (r < 0 or r > n) return 0; return fact[n] * ifact[r] * ifact[n - r]; } int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int n, s, l; cin >> n >> s >> l; if (n == 1) return cout << 1 << '\n', 0; init(s + n); Mint res = 0; for (int a = l; a <= s; ++a) for (int x = 1; x <= n; ++x) { if (a * x > s or a * x + (a - 1) * (n - x) < s) continue; Mint curr = 0; for (int k = 0; k <= n - x; ++k) { curr += (k & 1 ? -1 : 1) * comb(n - x, k) * comb(s - a * (x + k) + max(n - x - 1, 0), s - a * (x + k)); } curr *= comb(n - 1, x - 1); res += curr / x; } Mint sum = 0; for (int a = l; a <= s; ++a) { sum += comb(s - a + max(n - 2, 0), s - a); } res /= sum; cout << res << '\n'; }
#include <bits/stdc++.h> #pragma warning(disable : 4996) using namespace std; const int mod = 998244353; struct Mod { public: int num; Mod() : Mod(0) { ; } Mod(long long int n) : num((n % mod + mod) % mod) { static_assert(mod < INT_MAX / 2, "mod is too big, please make num 'long long int' from 'int'"); } Mod(int n) : Mod(static_cast<long long int>(n)) { ; } operator int() { return num; } }; Mod operator+(const Mod a, const Mod b) { return Mod((a.num + b.num) % mod); } Mod operator+(const long long int a, const Mod b) { return Mod(a) + b; } Mod operator+(const Mod a, const long long int b) { return b + a; } Mod operator++(Mod &a) { return a + Mod(1); } Mod operator-(const Mod a, const Mod b) { return Mod((mod + a.num - b.num) % mod); } Mod operator-(const long long int a, const Mod b) { return Mod(a) - b; } Mod operator--(Mod &a) { return a - Mod(1); } Mod operator*(const Mod a, const Mod b) { return Mod(((long long)a.num * b.num) % mod); } Mod operator*(const long long int a, const Mod b) { return Mod(a) * b; } Mod operator*(const Mod a, const long long int b) { return Mod(b) * a; } Mod operator*(const Mod a, const int b) { return Mod(b) * a; } Mod operator+=(Mod &a, const Mod b) { return a = a + b; } Mod operator+=(long long int &a, const Mod b) { return a = a + b; } Mod operator-=(Mod &a, const Mod b) { return a = a - b; } Mod operator-=(long long int &a, const Mod b) { return a = a - b; } Mod operator*=(Mod &a, const Mod b) { return a = a * b; } Mod operator*=(long long int &a, const Mod b) { return a = a * b; } Mod operator*=(Mod &a, const long long int &b) { return a = a * b; } Mod operator^(const Mod a, const int n) { if (n == 0) return Mod(1); Mod res = (a * a) ^ (n / 2); if (n % 2) res = res * a; return res; } Mod mod_pow(const Mod a, const long long int n) { if (n == 0) return Mod(1); Mod res = mod_pow((a * a), (n / 2)); if (n % 2) res = res * a; return res; } Mod inv(const Mod a) { return a ^ (mod - 2); } Mod operator/(const Mod a, const Mod b) { assert(b.num != 0); return a * inv(b); } Mod operator/(const long long int a, const Mod b) { return Mod(a) / b; } Mod operator/=(Mod &a, const Mod b) { return a = a / b; } Mod fact[10240], factinv[10240]; void init(const int amax = 10240) { fact[0] = Mod(1); factinv[0] = 1; for (int i = 0; i < amax - 1; ++i) { fact[i + 1] = fact[i] * Mod(i + 1); factinv[i + 1] = factinv[i] / Mod(i + 1); } } Mod comb(const int a, const int b) { return fact[a] * factinv[b] * factinv[a - b]; } int main() { init(); int N, S, R; cin >> N >> S >> R; Mod answer = 0; for (int num = 1; num <= N; ++num) { int rest = S - num * R; if (rest < 0) break; else { Mod nanswer = 0; nanswer = comb(N, num); nanswer *= comb(rest + N - 1, rest); Mod plus = Mod(num % 2 == 1 ? 1 : -1); answer += plus * nanswer; } } { Mod fst = 1; fst = comb(S - R + N - 1, N - 1); answer /= fst; answer /= N; } cout << answer.num << endl; return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 5500, mod = 998244353; int p, s, r, ans, fac[N], inv[N]; void exGCD(int a, int b, int &x, int &y) { if (!b) { x = 1, y = 0; return; } exGCD(b, a % b, y, x), y -= a / b * x; } int Inv(int x) { int xx, yy; exGCD(x, mod, xx, yy); return (xx % mod + mod) % mod; } void Prework() { fac[0] = inv[0] = 1; for (int i = 1; i <= 5200; i++) fac[i] = 1ll * fac[i - 1] * i % mod; inv[5200] = Inv(fac[5200]); for (int i = 5199; i; i--) inv[i] = 1ll * inv[i + 1] * (i + 1) % mod; } int C(int n, int m) { if (n == m) return 1; if (n < m) return 0; return 1ll * fac[n] * inv[m] % mod * inv[n - m] % mod; } int Calc(int cnt, int lim, int tot) { int ret = C(tot + cnt - 1, cnt - 1); for (int i = 1, j; i <= cnt; i++, ret %= mod) j = i % 2 ? mod - 1 : 1, ret += 1ll * j * C(cnt, i) % mod * C(tot - i * lim + cnt - 1, cnt - 1) % mod; return (ret + mod) % mod; } int main() { scanf("%d%d%d", &p, &s, &r), Prework(); for (int i = r; i <= s; i++) for (int j = 1; j <= p && i * j <= s; j++, ans %= mod) ans += 1ll * C(p - 1, j - 1) * Inv(j) % mod * Calc(p - j, i, s - i * j) % mod; printf("%lld", 1ll * ans * Inv(C(s - r + p - 1, p - 1)) % mod); return 0; }
#include <bits/stdc++.h> using namespace std; const int N = 10000; const int MOD = 998244353; int p, s, r; long long f[N + 10], invf[N + 10]; long long getInv(long long base) { long long ret = 1; int tmp = MOD - 2; while (tmp) { if (tmp & 1) ret = ret * base % MOD; base = base * base % MOD; tmp >>= 1; } return ret; } inline long long C(int m, int n) { if (m < n) return 0; return f[m] * invf[n] % MOD * invf[m - n] % MOD; } long long calc(int rest, int n, int ub) { if (!n) return (rest == 0); long long ret = 0; for (int i = 0; i <= n; i++) { long long tmp = C(rest - i * ub + n - 1, n - 1) * C(n, i) * ((i & 1) ? -1 : 1) % MOD; if (!tmp) break; ret = (ret + tmp) % MOD; } return ret; } int main() { ios::sync_with_stdio(false); cin >> p >> s >> r; f[0] = invf[0] = 1; for (int i = 1; i <= N; i++) { f[i] = f[i - 1] * i % MOD; invf[i] = getInv(f[i]); } long long ans = 0; for (int i = r; i <= s; i++) for (int j = 1; j <= p && i * j <= s; j++) { ans = (ans + C(p - 1, j - 1) * calc(s - i * j, p - j, i) % MOD * getInv(j)) % MOD; } ans = ans * getInv(C(s - r + p - 1, p - 1)) % MOD; cout << (ans + MOD) % MOD << "\n"; }
#include <bits/stdc++.h> using namespace std; const int sz = 10007; const int p = 998244353; int a[sz], b[sz], inv[sz]; void init() { a[0] = b[0] = 1; a[1] = b[1] = inv[1] = 1; for (int i = 2; i < sz; i++) { inv[i] = 1ll * (p - p / i) * inv[p % i] % p; a[i] = 1ll * a[i - 1] * i % p; b[i] = 1ll * b[i - 1] * inv[i] % p; } } int C(int n, int m) { if (n < m) return 0; if (n == 0) return 0; return 1ll * a[n] * b[m] % p * b[n - m] % p; } int qpow(int x, int y) { int ret = 1; for (; y; y >>= 1, x = 1ll * x * x % p) if (y & 1) ret = 1ll * ret * x % p; return ret; } int solve(int s, int m, int x) { int ret = 0; if (s == 0) return 1; for (int i = 0; i <= m && i * x <= s; i++) { int val = 1ll * C(m, i) * C(s - x * i + m - 1, m - 1) % p; ret = (ret + (i & 1 ? p - val : val)) % p; } return ret; } int main() { init(); int n, s, r; scanf("%d%d%d", &n, &s, &r); if (n == 1) { printf("1\n"); return 0; } int ans = 0; for (int x = r; x <= s; x++) { if (x * n < s) continue; for (int i = 1; i <= n; i++) { if (i * x > s || (n - i) * (x - 1) + i * x < s) continue; if (i == n) { ans = (ans + (i * x == s ? inv[i] : 0)) % p; continue; } ans = (ans + 1ll * solve(s - i * x, n - i, x) * C(n - 1, i - 1) % p * inv[i] % p) % p; } } int ny = qpow(C(s - r + n - 1, n - 1), p - 2); ans = 1ll * ans * ny % p; printf("%d", ans); }
#include <bits/stdc++.h> using namespace std; const int maxn = 103, maxs = 5003, mo = 998244353; int n, s, r, ans, C[maxn + maxs][maxn + maxs]; inline int qpow(int a, int b) { int res = 1; for (; b; b >>= 1, a = (long long)a * a % mo) if (b & 1) res = (long long)res * a % mo; return res; } inline int cbn(int a, int b) { if (a < b) return 0; if (b < 0 || a < 0) return 0; if (C[a][b]) return C[a][b]; return C[a][b] = (cbn(a - 1, b) + cbn(a - 1, b - 1)) % mo; } inline int getdp(int m, int sm, int x) { if (m == 0) return sm == 0; if (x == 0) return 0; int res = 0; for (register int i = 0; i <= m; ++i) if (i & 1) res = (res - (long long)cbn(m, i) * cbn(sm - x * i + m - 1, m - 1)) % mo; else res = (res + (long long)cbn(m, i) * cbn(sm - x * i + m - 1, m - 1)) % mo; return res; } int main() { scanf("%d%d%d", &n, &s, &r); C[0][0] = 1; for (register int i = r; i <= s; ++i) for (register int j = 1; j <= n; ++j) { ans = (ans + (long long)cbn(n - 1, j - 1) * getdp(n - j, s - i * j, i) % mo * qpow(j, mo - 2)) % mo; } ans = (long long)ans * qpow(cbn(s - r + n - 1, n - 1), mo - 2) % mo; if (ans < 0) ans += mo; printf("%d", ans); return 0; }
#include <bits/stdc++.h> using namespace std; long long nCr[5500][150]; const long long mod = (119 << 23) + 1, root = 3; long long modpow(long long a, long long e) { if (e == 0) return 1; long long x = modpow(a * a % mod, e >> 1); return e & 1 ? x * a % mod : x; } long long inv(long long a) { return modpow(a, mod - 2); } long long binom(long long n, long long k) { if (n == -1 && k == -1) return 1; if (k < 0 || k > n || n < 0) return 0; return nCr[n][k]; } int main() { nCr[0][0] = 1; for (int i = (1); i < int(5500); ++i) for (int j = (0); j < int(150); ++j) { nCr[i][j] = nCr[i - 1][j]; if (j) { nCr[i][j] += nCr[i - 1][j - 1]; nCr[i][j] %= mod; } } ios::sync_with_stdio(0); int p, s, r; cin >> p >> s >> r; long long succeeding = 0; long long total = 0; for (int a1 = (r); a1 < int(s + 1); ++a1) { total += binom(s + p - 2 - a1, p - 2); total %= mod; long long states = 0; vector<long long> counted(p); for (int numSame = (0); numSame < int(p); ++numSame) { if (s + p - numSame - 2 - (numSame + 1) * a1 < -1) break; for (int numLargerOrEqual = (0); numLargerOrEqual < int(p - numSame); ++numLargerOrEqual) { if (s + p - numSame - 2 - (numSame + 1 + numLargerOrEqual) * a1 < -1) break; long long mul = (numLargerOrEqual % 2 ? -1 : 1); long long t = mul * binom(p - 1, numSame); t *= binom(p - 1 - numSame, numLargerOrEqual); t %= mod; t *= binom(s + p - numSame - 2 - (numSame + 1 + numLargerOrEqual) * a1, p - 2 - numSame); t %= mod; t *= inv(numSame + 1); states += t; states %= mod; } } if (states < 0) states += mod; succeeding += states; succeeding %= mod; } long long ans = succeeding * inv(total); ans %= mod; cout << ans << endl; }
#include <bits/stdc++.h> using namespace std; const long MOD = 998244353; long long fact[6000], invfact[6000], inv[1000]; long long pow(long long a, long long n) { if (n == 0) return 1; long long p = pow(a, n / 2); p = (p * p) % MOD; return (n % 2 == 0 ? p : (a * p) % MOD); } long long modinv(long long a) { return pow(a, MOD - 2); } long long choose(int n, int k) { if (n < 0 || k < 0 || n < k) return 0; return (((fact[n] * invfact[k]) % MOD) * invfact[n - k]) % MOD; } long long g(int s, int p, int m) { if (p == 0) return (s == 0 ? 1 : 0); long long ans = 0; for (int k = 0; k <= p; k++) { ans += (k % 2 == 0 ? choose(p, k) : MOD - choose(p, k)) * choose(s - k * (m + 1) + p - 1, p - 1); ans %= MOD; } return ans; } int main() { int p, s, r; cin >> p >> s >> r; fact[0] = 1; invfact[0] = 1; for (int i = 1; i <= s + p - 1; i++) { fact[i] = (fact[i - 1] * i) % MOD; invfact[i] = modinv(fact[i]); } for (int i = 1; i <= p; i++) inv[i] = modinv(i); long long ans = 0; for (int a = r; a <= s; a++) { for (int k = 1; k <= p; k++) { ans += ((choose(p - 1, k - 1) * g(s - k * a, p - k, a - 1)) % MOD) * inv[k]; ans %= MOD; } } ans *= modinv(choose(s - r + p - 1, p - 1)); ans %= MOD; cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; void dbg_out() { cerr << endl; } template <typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cerr << ' ' << H; dbg_out(T...); } pair<int, int> operator*(const pair<int, int> &p, const pair<int, int> &x) { pair<int, int> np = make_pair(p.first * x.first, p.second * x.second); return np; } pair<long long, long long> operator%(const pair<long long, long long> &p, const pair<long long, long long> &x) { pair<long long, long long> np = make_pair(p.first % x.first, p.second % x.second); return np; } pair<long long, long long> operator*(const pair<long long, long long> &p, const pair<int, int> &x) { pair<long long, long long> np = make_pair(p.first * x.first, p.second * x.second); return np; } pair<long long, long long> operator*(const pair<long long, long long> &p, const pair<long long, long long> &x) { pair<long long, long long> np = make_pair(p.first * x.first, p.second * x.second); return np; } pair<long long, long long> operator+(const pair<long long, long long> &p, const pair<long long, long long> &x) { pair<long long, long long> np = make_pair(p.first + x.first, p.second + x.second); return np; } pair<long long, long long> operator-(const pair<long long, long long> &p, const pair<long long, long long> &x) { pair<long long, long long> np = make_pair(p.first - x.first, p.second - x.second); return np; } pair<int, int> operator+(const pair<int, int> &p, const pair<int, int> &x) { pair<int, int> np = make_pair(p.first + x.first, p.second + x.second); return np; } pair<int, int> operator-(const pair<int, int> &p, const pair<int, int> &x) { pair<int, int> np = make_pair(p.first - x.first, p.second - x.second); return np; } vector<int> prime; bool sortinrev(const pair<int, int> &a, const pair<int, int> &b) { return (a.first > b.first); } bool sortbysecdesc(const pair<int, int> &a, const pair<int, int> &b) { return a.second > b.second; } bool sortbysec(const pair<int, int> &a, const pair<int, int> &b) { return (a.second < b.second); } long long powerm(long long a, long long k) { if (!k) { return 1; } long long b = powerm(a, k / 2); b = b * b % 998244353; if (k % 2) { return a * b % 998244353; } else { return b; } } long long power(long long a, long long b) { if (b == 1) return a; if (b == 0) return 1; long long m1 = power(a, b / 2); if (b % 2) return m1 * m1 * a; return m1 * m1; } void PFactor(int x) { prime.clear(); for (int i = 2; i <= x / i; i++) if (x % i == 0) { while (x % i == 0) x /= i, prime.push_back(i); } if (x > 1) prime.push_back(x); } bool isprime(long long a) { if (a <= 1) return false; if (a == 2 || a == 3) return true; if (a % 2 == 0 || a % 3 == 0) return false; for (long long i = 5; i * i <= a; i = i + 6) { if (a % i == 0 || a % (i + 2) == 0) return false; } return true; } long long read() { long long a = 0; char b = 1, c; do if ((c = getchar()) == 45) b = -1; while (c < 48 || c > 57); do a = (a << 3) + (a << 1) + (c & 15); while ((c = getchar()) > 47 && c < 58); return a * b; } void write(long long x, char c) { if (x < 0) putchar(45), x = -x; char a[20], s = 0; do a[++s] = x % 10 | 48; while (x /= 10); do putchar(a[s]); while (--s); putchar(c); } const int N = 2e6 + 20; vector<int> g[N]; int n = 0, m = 0, s = 0; int d[N] = {0}; long long c[5201][5201]; inline long long f(int x, int sum, int maxx) { if (x * maxx < sum) return 0ll; if (x == 0 || sum == 0) return 1ll; long long ans = 0; for (int k = 0; k * (maxx + 1) <= sum && k <= x; k++) { if (k % 2) ans += (998244353 - ((c[sum - k * (maxx + 1) + x - 1][x - 1] * c[x][k]) % 998244353)); else ans += c[sum - k * (maxx + 1) + x - 1][x - 1] * c[x][k]; ans %= 998244353; } return ans; } int main() { for (int i = 0; i <= 5200; i++) { c[i][0] = 1; for (int j = 1; j <= i; j++) { c[i][j] = c[i - 1][j] + c[i - 1][j - 1]; c[i][j] %= 998244353; } } cin >> n >> s >> m; if (s == 0) { cout << powerm(n, 998244353 - 2ll); return 0; } long long ans = powerm(c[s - m + n - 1][n - 1], 998244353 - 2ll); m--; long long summ = 0; while (++m <= s) { if (m == 0) continue; for (int t = 1; t * m <= s; t++) { long long tans = powerm(t, 998244353 - 2ll); tans = (tans * f(n - t, s - t * m, m - 1)) % 998244353; tans = (tans * c[n - 1][t - 1]) % 998244353; summ += tans; summ %= 998244353; } } cout << (ans * summ) % 998244353; }
#include <bits/stdc++.h> using namespace std; const long long mod = 998244353; long long fac[10005], ifac[10005], n, s, r; inline long long Pow(long long x, long long y) { long long ret = 1; while (y) { if (y & 1) ret = ret * 1ll * x % mod; x = x * 1ll * x % mod; y >>= 1; } return ret % mod; } inline long long inv(long long x) { return Pow(x, mod - 2); } inline long long C(long long n, long long m) { if (m > n || m < 0) return 0; return fac[n] * 1ll * ifac[n - m] % mod * ifac[m] % mod; } inline long long F(long long n, long long m) { if (m < 0) return 0; return C(n + m - 1, n - 1); } inline long long Mod(long long x) { if (x >= mod) x -= mod; else if (x < 0) x += mod; return x; } inline long long F1(long long n, long long m, long long r) { if (!n && !m) return 1; long long ret = 0, sign = (n & 1) ? -1 : 1; for (long long i = 0; i <= n; ++i, sign *= -1) if (m - (r + 1) * (n - i) >= 0) (ret += sign * C(n, i) % mod * F(n, m - (r + 1) * (n - i)) % mod) %= mod; return ret; } int main() { fac[0] = 1; for (long long i = 1; i <= 10000; ++i) fac[i] = fac[i - 1] * 1ll * i % mod; ifac[10000] = Pow(fac[10000], mod - 2); for (long long i = 9999; i >= 0; --i) ifac[i] = ifac[i + 1] * 1ll * (i + 1) % mod; cin >> n >> s >> r; long long ans = 0; for (long long x = r; x <= s; ++x) { for (long long y = 0; (y + 1) * x <= s && y + 1 <= n; ++y) { long long m = n - y - 1, ss = s - (y + 1) * x; ans = Mod(ans + F1(m, ss, x - 1) * 1ll * C(n - 1, y) % mod * inv(y + 1) % mod); } } cout << ans * 1ll * inv(C(s - r + n - 1, n - 1)) % mod; return 0; }
#include <bits/stdc++.h> using namespace std; int Pow(int a, int b, int md, int ret = 1) { for (; b; b >>= 1, a = 1ll * a * a % md) { if (b & 1) ret = 1ll * ret * a % md; } return ret; } const int N = 5e4 + 10, MOD = 998244353; int first[N], I[N], inv[N], m, n, r; int C(int x, int y) { if (x < y || y < 0) return 0; return 1ll * first[x] * I[y] % MOD * I[x - y] % MOD; } int main() { scanf("%d%d%d", &n, &m, &r); first[0] = 1; for (int i = 1; i < N; i++) inv[i] = Pow(i, MOD - 2, MOD); for (int i = 1; i < N; i++) first[i] = 1ll * first[i - 1] * i % MOD; I[N - 1] = Pow(first[N - 1], MOD - 2, MOD); for (int i = N - 1; i; i--) { I[i - 1] = 1ll * I[i] * i % MOD; } int ret = 0; for (int i = 0; i < n; i++) { for (int j = r; j <= m; j++) { int a = n - i - 1, b = m - (i + 1) * j, c = j - 1; int tot = 0; if (b < 0) continue; if (!a) { tot = (!b); } else { for (int d = 0; d <= a; d++) { int x = 1ll * C(a, d) * C(a + b - 1 - d * (c + 1), a - 1) % MOD; tot = (tot + (d & 1 ? -x : x) + (d & 1) * MOD) % MOD; } } ret = (ret + 1ll * C(n - 1, i) * tot % MOD * inv[i + 1]) % MOD; } } ret = 1ll * ret * Pow(C(m + n - 1 - r, n - 1), MOD - 2, MOD) % MOD; printf("%d\n", ret); return 0; }
#include <bits/stdc++.h> using namespace std; int c[10007][5007]; const long long mod = 998244353; long long pown(long long a, long long b) { long long ans = 1; while (b) { if (b & 1) ans = (ans * a) % mod; a = (a * a) % mod; b >>= 1; } return ans; } int C(int x, int y) { if (x < 0 || y < 0) return 0; else return c[x][y]; } int main() { int n, s, r; scanf("%d%d%d", &n, &s, &r); if (n == 1) { printf("1"); return 0; } c[0][0] = 1; for (int i = 1; i <= 10000; i++) { c[i][0] = 1; for (int k = 1; k <= min(i, 5000); k++) c[i][k] = (c[i - 1][k] + c[i - 1][k - 1]) % mod; } long long x = 0, y = 0; for (int i = r; i <= s; i++) { int end = (i == 0) ? n : min(s / i, n); for (int k = 1; k <= end; k++) { if (k == n) { long long sum = (k * i == s); x += sum; x %= mod; y += (sum * pown(k, mod - 2)) % mod; y %= mod; continue; } int flag = 1; long long now = 0; for (int z = 0; z <= end - k; z++) { now += C(n - k, z) * (C(s - i * (k + z) + n - k - 1, n - k - 1) * flag + mod) % mod; now %= mod; flag = -flag; } now *= C(n - 1, k - 1); now %= mod; now = (now * pown(k, mod - 2)) % mod; y += now; y %= mod; } } printf("%lld", y * pown(C(s - r + n - 1, n - 1), mod - 2) % mod); return 0; }
#include <bits/stdc++.h> using namespace std; long long ksm(long long x, long long t) { long long ans = 1; for (; t; t >>= 1, x = (x * x) % 998244353) if (t & 1) ans = (ans * x) % 998244353; return ans; } int p, s, r; long long fac[6005], invf[6005]; void pre() { fac[0] = 1; for (int i = 1; i <= p + s; i++) fac[i] = (fac[i - 1] * i) % 998244353; invf[p + s] = ksm(fac[p + s], 998244353 - 2); for (int i = p + s - 1; i >= 0; i--) invf[i] = (invf[i + 1] * (i + 1)) % 998244353; } long long C(long long n, long long m) { if (n < 0 || m < 0 || m > n) return 0; return ((fac[n] * invf[n - m]) % 998244353 * invf[m]) % 998244353; } long long ans; long long g(long long s, long long p, long long m) { if (p == 0 && s == 0) return 1; long long tot = 0; for (int i = 0, t = 1; i <= p; i++) { tot += t * (C(p, i) * C(s + p - 1 - i * (m + 1), p - 1) % 998244353); tot = (tot + 998244353) % 998244353; t *= -1; } return tot; } int main() { scanf("%d%d%d", &p, &s, &r); pre(); for (int t = r; t <= s; t++) for (int q = 1; q <= p; q++) { ans += ((C(p - 1, q - 1) * ksm(q, 998244353 - 2) % 998244353) * g(s - q * t, p - q, t - 1)) % 998244353; ans %= 998244353; } ans *= ksm(C(s + p - 1 - r, p - 1), 998244353 - 2); ans %= 998244353; printf("%lld", ans); return 0; }
#include <bits/stdc++.h> using namespace std; long long poww(long long x, long long y) { long long res = 1; while (y > 0) { if (y & 1) res = (res * x) % 998244353ll; y = y >> 1; x = (x * x) % 998244353ll; } return res; } long long p, s, r; long long fac[100005], inv[100005], num[100005]; long long func(long long, long long, long long), calc(long long, long long, long long), C(long long, long long); int main() { cin >> p >> s >> r; fac[0] = inv[0] = 1; for (int i = 1; i < 10005; i++) { num[i] = poww(i, 998244353ll - 2); fac[i] = (fac[i - 1] * i) % 998244353ll; inv[i] = poww(fac[i], 998244353ll - 2); } long long ans = 0, div = poww(C(s - r + p - 1, s - r), 998244353ll - 2); for (int i = r; i < s + 1; i++) { ans = (ans + func(p, s, i)) % 998244353ll; } cout << ((ans * div) % 998244353ll); } long long func(long long p, long long s, long long top) { long long ans = 0; for (int i = 0; i < p; i++) { long long rem = s - (i + 1) * top; long long left = (p - i - 1); if (rem < 0 || left * (top - 1) < rem) continue; ans = (ans + num[i + 1] * C(p - 1, i) % 998244353ll * calc(left, rem, top) % 998244353ll) % 998244353ll; } return ans; } long long calc(long long left, long long rem, long long top) { long long ans = 0; long long p = 1; for (int i = 0; i < rem + 1; i++) { long long rr = (rem - top * i); if (rr < 0) break; ans = ((ans + p * C(left, i) * (rr == 0 ? 1 : C(left - 1 + rr, rr))) % 998244353ll + 998244353ll) % 998244353ll; p *= -1; } return ans; } long long C(long long x, long long y) { return fac[x] * inv[y] % 998244353ll * inv[x - y] % 998244353ll; }
#include <bits/stdc++.h> using namespace std; const long long mod = 998244353; int n, S, r; long long C[5205][5205], ans; long long power(long long x, long long y) { long long ret = 1; for (; y; y >>= 1, x = x * x % mod) if (y & 1) ret = ret * x % mod; return ret; } long long inv(long long x) { return power(x, mod - 2); } int main() { C[0][0] = 1; for (int i = 1; i <= 5200; i++) { C[i][0] = 1; for (int j = 1; j <= i; j++) C[i][j] = (C[i - 1][j] + C[i - 1][j - 1]) % mod; } scanf("%d%d%d", &n, &S, &r); for (int i = r; i <= S; i++) for (int j = 0; j < n; j++) { int rest = S - (j + 1) * i; long long tmp = 0; if (j + 1 == n) tmp = (rest == 0); else { for (int k = 0; k <= n - j - 1; k++) if (rest - k * i >= 0) { if (k & 1) tmp = (tmp - C[n - j - 1][k] * C[rest - k * i + n - j - 2][n - j - 2] % mod + mod) % mod; else tmp = (tmp + C[n - j - 1][k] * C[rest - k * i + n - j - 2][n - j - 2] % mod) % mod; } } ans = (ans + tmp * C[n - 1][j] % mod * inv(j + 1)) % mod; } printf("%lld\n", ans * inv(C[S - r + n - 1][n - 1]) % mod); return 0; }
#include <bits/stdc++.h> using namespace std; const int mod = 998244353; const int maxn = 10000 + 10; long long mypow(long long x, long long res) { if (res == 0) return 1; long long cur = mypow(x, res >> 1); cur = cur * cur % mod; if (res & 1) cur = cur * x % mod; return cur; } long long fac[maxn], rev[maxn]; void pre() { fac[0] = fac[1] = rev[0] = rev[1] = 1; for (int i = 2; i < maxn; i++) { fac[i] = fac[i - 1] * i % mod; rev[i] = ((mod - mod / i * rev[mod % i]) % mod + mod) % mod; } for (int i = 2; i < maxn; i++) rev[i] = rev[i - 1] * rev[i] % mod; } long long C(int m, int n) { if (m < n) return 0; return fac[m] * rev[n] % mod * rev[m - n] % mod; } long long cal(int n, int lim, int s) { if (s < 0 || lim == 0) return 0; if (n == 0) return s == 0; long long ans = 0; for (int i = 0; i <= min(n, s / lim); i++) { if (i & 1) ans = ((ans - C(n, i) * C(s - i * lim + n - 1, n - 1)) % mod + mod) % mod; else ans = (ans + C(n, i) * C(s - i * lim + n - 1, n - 1)) % mod; } return ans; } int main() { pre(); int p, s, r; scanf("%d%d%d", &p, &s, &r); if (s == 0) { printf("%lld", rev[p] * fac[p - 1] % mod); return 0; } long long ans = 0; for (int i = r; i <= s; i++) for (int j = 1; j <= p; j++) ans = (ans + C(p - 1, j - 1) * cal(p - j, i, s - i * j) % mod * rev[j] % mod * fac[j - 1]) % mod; ans = ans * mypow(cal(p, s + 1, s - r), mod - 2) % mod; printf("%lld", ans); return 0; }
#include <bits/stdc++.h> using namespace std; long long power(long long b, long long e, long long m) { if (e == 0) return 1; if (e & 1) return b * power(b * b % m, e / 2, m) % m; return power(b * b % m, e / 2, m); } long long power(long long b, long long e) { if (e == 0) return 1; if (e & 1) return b * power(b * b, e / 2); return power(b * b, e / 2); } long long inv[10000 + 5], fac_inv[10000 + 5], fac[10000 + 5]; void initialize() { long long i; inv[1] = 1; for (i = 2; i <= 10000; i++) inv[i] = (998244353 - 998244353 / i) * inv[998244353 % i] % 998244353; fac[0] = fac[1] = 1; for (i = 2; i <= 10000; i++) fac[i] = i * fac[i - 1] % 998244353; fac_inv[0] = fac_inv[1] = 1; for (i = 2; i <= 10000; i++) fac_inv[i] = inv[i] * fac_inv[i - 1] % 998244353; } long long ncr(long long n, long long r) { if (n < 0 || r < 0) return 0; if (n < r) return 0; return (fac[n] * fac_inv[r] % 998244353) * fac_inv[n - r] % 998244353; } long long solve(long long sc, long long n, long long s) { if (s < 0) return 0; if (n == 0 && s == 0) return 1LL; long long ret = ncr(s + n - 1, n - 1); for (long long i = 1; i <= n; ++i) { long long kk = ncr(s - i * sc + n - 1, n - 1); kk *= ncr(n, i); kk %= 998244353; if (i & 1) ret -= kk; else ret += kk; ret += 998244353; ret %= 998244353; } return ret; } int _runtimeTerror_() { long long p, s, r, i; cin >> p >> s >> r; long long ans = 0; for (i = r; i <= s; ++i) { for (long long j = 1; j <= p; ++j) { long long fuck = solve(i, p - j, s - i * j); ans += fuck * power(j, 998244353 - 2, 998244353) % 998244353 * ncr(p - 1, j - 1) % 998244353; ans %= 998244353; } } long long tt = ncr(s - r + p - 1, p - 1); cout << ans * power(tt, 998244353 - 2, 998244353) % 998244353 << "\n"; return 0; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); initialize(); int TESTS = 1; while (TESTS--) _runtimeTerror_(); return 0; }
#include <bits/stdc++.h> using namespace std; long long mod = 998244353; long long cd, s, r, fact[10001], sf[10001], invmod[10001]; void inp() { cin >> cd >> s >> r; } long long bigmod(long long base, long long hat) { if (hat == 0) return 1; long long k = bigmod(base, hat / 2); if (hat % 2 == 0) return k * k % mod; return k * k % mod * base % mod; } void create() { for (long long i = 0; i <= 10000; i++) { if (i == 0) fact[i] = 1; else fact[i] = fact[i - 1] * i % mod; sf[i] = bigmod(fact[i], mod - 2); invmod[i] = bigmod(i, mod - 2); } } long long C(long long k, long long n) { if (k > n || k < 0 || n < 0) return 0; return fact[n] * sf[k] % mod * sf[n - k] % mod; } void do_it() { create(); long long all = 0, kq = 0; for (long long i = r; i <= s; i++) { all += C(cd - 2, s - i + cd - 1 - 1); all %= mod; if (cd * i == s) kq += invmod[cd], kq %= mod; for (long long e = 1; e < cd; e++) { if (e * i > s) break; long long remain = s - e * i, inv = 0; remain += cd - e; long long space = C(e - 1, cd - 1) * C(cd - e - 1, remain - 1) % mod; for (long long f = 1; f <= cd - e; f++) { long long t = remain - i * f; if (t < 0 || cd - e - 1 > t - 1) break; if (f % 2 == 1) inv += C(cd - e - 1, t - 1) * C(f, cd - e) % mod; else inv -= C(cd - e - 1, t - 1) * C(f, cd - e) % mod; inv += mod * 5, inv %= mod; } inv *= C(cd - e, cd - 1); space -= inv, space += mod * 5, space %= mod; kq += space * invmod[e] % mod, kq %= mod; } } if (cd == 1) kq = 1, all = 1; cout << kq * bigmod(all, mod - 2) % mod << endl; } int main() { inp(); do_it(); }
#include <bits/stdc++.h> using namespace std; template <typename T> inline void ckmax(T& x, T y) { x = (y > x ? y : x); } template <typename T> inline void ckmin(T& x, T y) { x = (y < x ? y : x); } const int MAXN = 100, MAXM = 5000; const int MOD = 998244353; inline int mod1(int x) { return x < MOD ? x : x - MOD; } inline int mod2(int x) { return x < 0 ? x + MOD : x; } inline void add(int& x, int y) { x = mod1(x + y); } inline void sub(int& x, int y) { x = mod2(x - y); } inline int pow_mod(int x, int i) { int y = 1; while (i) { if (i & 1) y = (long long)y * x % MOD; x = (long long)x * x % MOD; i >>= 1; } return y; } int fac[MAXM + MAXN + 5], ifac[MAXM + MAXN + 5]; inline int comb(int n, int k) { if (n < k) return 0; return (long long)fac[n] * ifac[k] % MOD * ifac[n - k] % MOD; } void facinit(int lim) { fac[0] = 1; for (int i = 1; i <= lim; ++i) fac[i] = (long long)fac[i - 1] * i % MOD; ifac[lim] = pow_mod(fac[lim], MOD - 2); for (int i = lim - 1; i >= 0; --i) ifac[i] = (long long)ifac[i + 1] * (i + 1) % MOD; } int n, m, low; int main() { facinit(MAXM + MAXN); cin >> n >> m >> low; int ans = 0; for (int v = low; v <= m; ++v) { for (int i = 1; i < n; ++i) { if (i * v > m) break; int curans = 0; for (int j = 0; j <= n - i; ++j) { if ((i + j) * v > m) break; int tmp = (long long)comb(n - 1, i - 1) * comb(n - i, j) % MOD * comb(m - (i + j) * v + (n - i) - 1, n - i - 1) % MOD; if (j & 1) sub(curans, tmp); else add(curans, tmp); } add(ans, (long long)curans * ifac[i] % MOD * fac[i - 1] % MOD); } if (n * v == m) { add(ans, (long long)ifac[n] * fac[n - 1] % MOD); } } ans = (long long)ans * pow_mod(comb(m - low + n - 1, n - 1), MOD - 2) % MOD; cout << ans << endl; return 0; }
#include <bits/stdc++.h> using namespace std; inline int setBit(int N, int pos) { return N = N | (1 << pos); } inline int resetBit(int N, int pos) { return N = N & ~(1 << pos); } inline bool checkBit(int N, int pos) { return (bool)(N & (1 << pos)); } const long long int MOD = 998244353; inline long long int add(long long int a, long long int b) { a += b; if (a >= MOD) a -= MOD; return a; } inline long long int sub(long long int a, long long int b) { a -= b; if (a < 0) a += MOD; return a; } inline long long int mul(long long int a, long long int b) { a *= b; a %= MOD; return a; } long long int fact[100010], inv[100010]; long long int nCr(int n, int r) { if (r > n) return 0; long long int ret = mul(inv[r], inv[n - r]); ret = mul(ret, fact[n]); return ret; } long long int f(int n, int k) { if (k == 0) return 1; return nCr(n + k - 1, n - 1); } long long int g(int n, int make, int high) { if (n == 0 && make == 0) return 1; if (high < 0) return 0; if (make < 0) return 0; if (high * n < make) return 0; if (make == 0) return 1; long long int ret = f(n, make); for (int i = 1; i <= n; i++) { long long int done = i * (high + 1); if (done > make) break; long long int cur = mul(nCr(n, i), f(n, make - done)); if (i & 1) ret = sub(ret, cur); else ret = add(ret, cur); } return ret; } long long int exp(int a, int b) { if (b == 0) return 1; if (b & 1) return mul(a, exp(a, b - 1)); long long int ret = exp(a, b / 2); return mul(ret, ret); } long long int I[100010]; int main() { fact[0] = inv[0] = I[0] = 1; for (int i = 1; i <= 100000; i++) fact[i] = mul(fact[i - 1], i), inv[i] = exp(fact[i], MOD - 2), I[i] = exp(i, MOD - 2); int n, sum, low; scanf("%d %d %d", &n, &sum, &low); if (n == 1) { printf("1\n"); return 0; } long long int total = 0; long long int ans = 0; for (int i = low; i <= sum; i++) { total = add(total, f(n - 1, sum - i)); ans = add(ans, g(n - 1, sum - i, i - 1)); for (int k = 2; k <= n; k++) { if (i * k > sum) break; long long int nw = mul(g(n - k, sum - (i * k), i - 1), nCr(n - 1, k - 1)); nw = mul(nw, I[k]); ans = add(ans, nw); } } ans = mul(ans, exp(total, MOD - 2)); cout << ans << endl; return 0; }